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The Works of Bronisław Knaster (1893–1980) in Continuum Theory

  • Janusz J. Charatonik
Part of the History of Topology book series (HIPO, volume 1)

Abstract

The principal area of the mathematical research of Bronisław Knaster (see the bibliography enclosed with this article) was geometric topology, and his main object of interest was connectedness. The greater part of this topic was related to the study of continua, which were then defined as closed and connected subsets of a Euclidean space, and were not necessarily compact.

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Bibliography of the works of Bronisław Knaster

  1. [K1]
    Bronisław Knaster: Bronisław Knaster: (with K. Kuratowski) Sur les ensembles connexes, Fundamenta Mathematicae 2 (1921), 206–255.Google Scholar
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    Bronisław Knaster: Bronisław Knaster: (with W. Sierpiriski) Sur une ensemble abstrait, dont chaque élément est un élément limite de chaque sous ensemble non dénombrable, Fundamenta Mathematicae 3 (1922), 35–40.Google Scholar
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    Bronisław Knaster: Bronisław Knaster: Un continu dont tout sous-continu est indécomposable, Fundamenta Mathematicae 3 (1922), 247–286.Google Scholar
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    Bronisław Knaster: Bronisław Knaster: (with K. Kuratowski) Sur les continus non bornés, Fundamenta Mathematicae 5 (1924), 23–58.Google Scholar
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    Bronisław Knaster: Bronisław Knaster: Sur un problème de M. R. L. Wilder, Fundamenta Mathematicae 7 (1925), 191–197.Google Scholar
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    Quelques coupures singulières du plan, Fundamenta Mathematicae 7 (1925), 264–289.Google Scholar
  7. [K7] Bronisław Knaster: (with K. Kuratowski)
    Sur quelques propriétés topologiques des functions dérivées, Rendiconti del Circolo Matematico di Palermo 49 (1925), 382–386.CrossRefGoogle Scholar
  8. [K8]
    Bronisław Knaster: Sur les ensembles connexes irréductibles entre deux points, Fundamenta Mathematicae 10 (1927), 276–297.Google Scholar
  9. [K9] Bronisław Knaster: (with K. Kuratowski)
    Remark on a theorem of R. L. Moore, Proceedings of the National Academy of Sciences U.S.A. 13 (1927), 647–649.CrossRefGoogle Scholar
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    Bronisław Knaster: (with K. Kuratowski)A connected and connected im kleinen point set which contains no perfect subset, Bulletin of the American Mathematical Society 33 (1927), 106–109.MathSciNetCrossRefGoogle Scholar
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    Bronisław Knaster: Decomposizioni continue e semicontinue nell’Analysis Situs, Atti del Congresso Internazionale dei Matematici in Bologna,1928, tomo II, 221–224.Google Scholar
  12. [K12]
    Bronisław Knaster: Sui punti regolari nelle curve di Jordan, Atti del Congresso Internazionale dei Matematici in Bologna,1928, tomo II, 225–227.Google Scholar
  13. [K13]
    Bronisław Knaster: Sur les continus que tout sous-continu divise, Ksigga Pamigtkowa I Polskiego Zjazdu Matematycznego we Lwowie [Memorial Book of the First Polish Mathematical Congress], Lwów 1929, 59–64.Google Scholar
  14. [K14]
    Bronisław Knaster: Einige Probleme über Punktmengen mit Fixpunkten, Comptes-Rendus du Premier Congrès des Mathématiciens des Pays Slaves, Warszawa 1929, 287–290.Google Scholar
  15. [K15] Bronisław Knaster: (with K. Kuratowski and S. Mazurkiewicz)
    Ein Beweis des Fixpunktsatzes für ri-dimensionale Simplexe, Fundamenta Mathematicae 14 (1929), 132–137.Google Scholar
  16. [K16]
    Über eindimensional unvergleichbare Kontinua, Anzeiger Wiener Akademie der Wissenschaften, Math.-naturwiss. Kl. Nr 10 (1930), 1–2.Google Scholar
  17. [K17]
    Bronisław Knaster: Ein Zerlegungssatz über unikohärente continua, Verhandlungen des Internationalen Mathematikerkongress in Zürich, Zürich 1932, 193–194.Google Scholar
  18. [K18]
    Bronisław Knaster: Pfehled teorie nerozlozitelnÿch kontinui [Survey of the theory of indecomposable continua], Casopis pro péstovâni matematiky a fizyky 62 (1933), 310–337. [in Czech; French summary].Google Scholar
  19. [K19]
    Bronisław Knaster: (with S. Mazurkiewicz) Sur un problème concernant les transformations continues, Fundamenta Mathematicae 21 (1933), 85–90.Google Scholar
  20. [K20]
    Bronisław Knaster: (with W. Hurewicz) Ein Einbettungssatz über henkelfreie Kontinua, Proceedings of the Section of Sciences, Koninklijke Akademie van Wetenschappen te Amsterdam 36 (1933), 557–560.Google Scholar
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    Bronisław Knaster: Un continu irréductible à décomposition continue en tranches, Fundamenta Mathematicae 25 (1935), 58–577.Google Scholar
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    Bronisław Knaster: Über rationale Kurven ohne Bögen, Monatshefte für Mathematik und Physik 42 (1935), 37–44.zbMATHCrossRefGoogle Scholar
  23. [K23]
    Bronisław Knaster: Sur une propriété caractéristique de l’ensemble des nombres réels, Matematicheskii SbornikAkademii Nauk SSSR 16 (58) (1945), 281–290.Google Scholar
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    Bronisław Knaster: Sur un problème de R. Alexandroff, Fundamenta Mathematicae 33 (1945), 308–313.MathSciNetzbMATHGoogle Scholar
  25. [K25]
    Bronisław Knaster: Sur les coupures biconnexes des espaces euclidiens de dimension n = 1 arbitraire, Matematicheskii Sbornik Akademii Nauk SSSR 19 (61) (1946), 9–18. [in Russian; loose French summary].Google Scholar
  26. [K26]
    Bronisław Knaster: with H. Steinhaus) Sur les partage pragmatique, Comptes Rendus de la Société des Sciences et des Lettres de Wroclaw 2 (1947), 1–13.Google Scholar
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    Bronisław Knaster: O drukarniach naukowych w Polsce [On scientific printing houses in Poland], Casopis pro péstovCni matematiky a fizyky 74 (1949), 341–346. [in Polish]Google Scholar
  28. [K28]
    Bronisław Knaster: O aplikacich matematické logiky na matematiku [On applications of mathematical logic in mathematics], Casopis pro péstovkni matematiky a fizyky 76 (1951) 3–22. [in Czech].Google Scholar
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    Bronisław Knaster: Sur une équivalence pour les fonctions, Colloquium Mathematicum 2 (1951), 1–4.Google Scholar
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    Bronisław Knaster: Un théorème sur la compactification, Annales de la Société Polonaise de Mathématique 25 (1952), 252–267.Google Scholar
  31. [K31]
    Bronisław Knaster: (with M. Reichbach)Sur la caractérisation topologique de l’ensemble des bouts d’une courbe, Fundamenta Mathematicae 40 (1953), 13–28.MathSciNetGoogle Scholar
  32. [K32]
    Bronisław Knaster: (with M. Reichbach) Un lemme sur les F-sigma, Fundamenta Mathematicae 40 (1953), 172–179.MathSciNetGoogle Scholar
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    Bronisław Knaster: (with M. Reichbach) Notion d’homogénéité et prolongements des homéomorphies, Fundamenta Mathematicae 40 (1953), 180–193.MathSciNetGoogle Scholar
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    Bronisław Knaster: (with K. Urbanik) Sur les espaces complets séparables de dimension 0, Fundamenta Mathematicae 40 (1953), 194–202.MathSciNetGoogle Scholar
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    Bronisław Knaster: Wspomnienie o Samuelu Dicksteinie [Samuel Dickstein — a memoir], Prace Matematyczne 1 (1955), 4–8. [in Polish]Google Scholar
  36. [K36]
    with J. Mioduszewski and K. Urbanik) Points-limites et points de continuité, Colloquium Mathematicum 3 (1955), 164–169.MathSciNetGoogle Scholar
  37. [K37]
    K37] Bronisław Knaster: Sur la fixation des décompositions, Bulletin de l’Académie Polonaise des Sciences, Cl. III,4 (1956) 193–196 . [a version in Russian on pp. 189–192] Bronisław Knaster: .Google Scholar
  38. [K38]
    Bronisław Knaster: (with A. Lelek) Coutures et tapis, Fundamenta Mathematicae 45 (1958), 186–199.MathSciNetGoogle Scholar
  39. [K39]
    Bronisław Knaster: (with J. Mioduszewski Division des régions partielles par les frontières et des frontières par les points, Fundamenta Mathematicae 45 (1958), 306–313.MathSciNetGoogle Scholar
  40. [K40]
    Bronisław Knaster: (with A. Lelek and J. Mycielski) Sur les décompositions d’ensembles connexes, Colloquium Mathematicum 6 (1958), 227–246.MathSciNetGoogle Scholar
  41. [K41]
    Bronisław Knaster: Eduard tech (1893–1960), Sprawozdania Wroctawskiego Towarzystwa Naukowego 15 B (1960), 6 –13. [in Polish].Google Scholar
  42. [K42]
    Bronisław Knaster: 101 posiedzenie naukowe Wydzialu Nauk Matematycznych i Przyrodniczych [101St scientific meeting of the Section of Mathematical and Natural Sciences], Sprawozdania Wroctawskiego Towarzystwa Naukowego 15 B (1960), 14–16. [in Polish].Google Scholar
  43. [K43]
    Bronisław Knaster: Zygmunt Janiszewski (1888–1920) [Preface in the book: Z. Janiszewski, Oeuvres choisies],PWN, Warszawa 1961; pp. 5–16. [in French; Polish translation in: Wiadomosci Matematyczne 4 (1960), 1–9.Google Scholar
  44. [K44]
    Bronisław Knaster: O pracach topologicznych katedry geometrii Uniwersytetu Wroclawskiego i seminarium topologii Instytutu Matematycznego PAN, Czggé I [On topological papers of the Chair of Geometry of the University of Wroclaw and Topological Seminar of the Mathematical Institute of the Polish Academy of Sciences, Part I], Sprawozdania Wroclawskiego Towarzystwa Naukowego 16B (1961), 6–7; Czggé II [Part II] ibidem,22. [in Polish].Google Scholar
  45. [K45]
    Bronisław Knaster: Karol Borsuk, Nauka Polska 3 1964, 61–65. [in Polish].Google Scholar
  46. [K46]
    Bronisław Knaster: (with S. Bergman, R. Duda, J. Mycielski and A. Schinzel) Kazimierz Zarankiewicz, Colloquium Mathematicum 12 (1964), 277–288. [in French; Polish translation in: Wiadomosci Matematyczne 9 (1967), 175–185.Google Scholar
  47. [K47]
    Bronisław Knaster: Une décomposition effective du carré en deux ensembles denses, ponctiformes, connexes et localement connexes, Commentationes Mathematicae (Prace Matematyczne) 14 (1970), 19–23.Google Scholar
  48. [K48]
    Bronisław Knaster: Poglady Stanislawa Kulczyrískiego na rolg matematyki w naukach przyrodniczych [Stanislaw Kulczyríski’s opinions on role of mathematics in natural sciences], Sprawozdania Wroclawskiego Towarzystwa Naukowego 30 A (1975), Dodatek 1, 126–127. [in Polish].Google Scholar
  49. [K49]
    Bronisław Knaster: A singular plane curve, Colloquium Mathematicum 42 (1979), 263–271.MathSciNetGoogle Scholar
  50. [K50]
    Bronisław Knaster: Sur un problème de M. L. Vietoris, Annales de la Société Polonaise de Mathématique 5 (1926), 102. [a report].Google Scholar
  51. [K51]
    Sur la théorie des dimensions de Menger-Urysohn, Annales de la Société Polonaise de Mathématique 6 (1927), 121–122. [a report].Google Scholar
  52. [K52]
    Bronisław Knaster: Un théorème sur trois continus plans, Annales de la Société Polonaise de Mathématique 6 (1927), 131. [a report].Google Scholar
  53. [K53]
    Bronisław Knaster: Un théorème sur les fonctions d’ensemble, Annales de la Société Polonaise de Mathématique 6 (1927), 133–134. [a report].Google Scholar
  54. [K54]
    Bronisław Knaster: Sur une courbe ne contenant aucune image continue d’intervalle ni aucun continu indécomposable, Comptes-Rendus du Premier Congrès des Mathématiciens des Pays Slaves,Warszawa 1929, 290. [an announcement].Google Scholar
  55. [K55]
    Une fonction réelle continue de deux variables qui n’est constante sur aucun arc simple [Announcement at the All-Union Congress on the Theory of Functions held in Kiev, 24–26 June 1940] Bronisław Knaster: .Google Scholar
  56. [K56]
    Sur une propriété caractéristique de l’ensemble des nombres réelles, List of the works achieved in the field of mathematics and sciences in Poland during the German occupation, 1939–1945, Polish Academy of Sciences and Letters,Krakow 1947, 224–225. [a report on [K23] Bronisław Knaster: ].Google Scholar
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    Bronisław Knaster: Une fonction réelle continue de deux variables réelles qui n’est constante sur aucun arc simple, List of the works achieved in the field of mathematics and sciences in Poland during the German occupation, 1939–1945, Polish Academy of Sciences and Letters,Krakow 1947, 225. [a report on [K55] Bronisław Knaster: ].Google Scholar
  58. [K58]
    Bronisław Knaster: Sur les coupures biconnexes des espaces euclidiens de dimension ri 1 arbitraire, List of the works achieved in the field of mathematics and sciences in Poland during the German occupation, 1939–1945, Polish Academy of Sciences and Letters,Krakow 1947, 225–227.Google Scholar
  59. [K59]
    Bronisław Knaster: Sur les ensembles connexes, Annales de la Société Polonaise de Mathématique 19 (1946), 223. [a report].Google Scholar
  60. [K60]
    Bronisław Knaster: Sur le problème du partage pragmatique de H. Steinhaus, Annales de la Société Polonaise de Mathématique 19 (1946 ), 228–230. [a report; loose summary of [K26] [also: Colloquium Mathematicum 1 (1948), 36].Google Scholar
  61. [K61]
    Bronisław Knaster: Sur les transformations continues des sphères en hyperplans de dimension inférieure, Annales de la Société Polonaise de Mathématique 19 (1946), 232. [a report] [also: Colloquium Mathematicum 1 (1948), 37.Google Scholar
  62. [K62]
    Bronisław Knaster: (with H. Steinhaus) O podziale pragmatycznym, Sprawozdania Wroctawskiego Towarzystwa Naukowego 2 (1947), 81–82. [in Polish; a summary of [K26].Google Scholar
  63. [K63]
    Bronisław Knaster: Rapport du voyage de Tchecoslovaquie, Colloquium Mathematicum 1 (1948), 41–42. [a report].Google Scholar
  64. [K64]
    Bronisław Knaster: Un problème sur les bandes inscrites, Gasopis pro péstovkni matematiky a fizyky 74 (1949), 236–237. [an announcement].Google Scholar
  65. [K65]
    Bronisław Knaster: N. I. Lobatchewsky, Colloquium Mathematicum 2 (1951), 159. [a report].Google Scholar
  66. [K66]
    Sur l’ensemble des points d’orde 1 au sens de Menger, Colloquium Mathematicum 2 (1951), 311. [a report].Google Scholar
  67. [K67]
    Bronisław Knaster: Sur un problème de Borsuk, Colloquium Mathematicum 2 (1951), 323. [a report].Google Scholar
  68. [K68]
    Bronisław Knaster: Sur un continu irréductible construit par J. Mioduszewski, Colloquium Mathematicum 3 (1955), 82. [a report].Google Scholar
  69. [K69]
    Bronisław Knaster: Un théorème sur la compactification, Colloquium Mathematicum 3 (1955), 188. [a report].Google Scholar
  70. [K70]
    Bronisław Knaster: (with M. Reichbach) Un lemme sur les F-sigma, Colloquium Mathematicum 3 (1955), 200. [a report]also: Prace Matematyczne 1 (1955), 194.Google Scholar
  71. [K71]
    Bronisław Knaster: Un problème sur la piste des faces d’un tertaèdre roulant sur le plan, Colloquium Mathematicum 3 (1955), 203. [a report].Google Scholar
  72. [K72]
    Bronisław Knaster: (with K. Urbanik) Sur les espaces complets de dimension 0, Colloquium Mathematicum 3 (1955), 206. [a report] also: Prace Matematyczne 1 (1955), 198.Google Scholar
  73. [K73]
    Bronisław Knaster: (with J. Mioduszewski and K. Urbanik) Points-limites et points de continuité, Colloquium Mathematicum 3 (1955), 210. [a report] [also: Prace Matematyczne 1 (1955), 200 .Google Scholar
  74. [K74]
    Bronisław Knaster: Un théorème sur les décompositions semi-continues, Colloquium Mathematicum 4 (1957), 137. [a report].Google Scholar
  75. [K75]
    Bronisław Knaster: Sur certaines bases dans les cubes a n dimensions, Colloquium Mathematicum 4 (1957), 138–139. [a report].Google Scholar
  76. [K76]
    Sur le problème du rapport entre fixation et enfilage, Colloquium Mathematicum 4 (1957), 267. [a report] also: Prace Matematyczne 2 (1958), 197.Google Scholar
  77. [K77]
    Bronisław Knaster: (with J. Mioduszewski) O dzieleniu obszarów czgsciowych przez brzegi i brzegow przez punkty [On divisions of partial regions by boundaries and boundaries by points], Prace Matematyczne 4 (1960), 137. [a report].Google Scholar
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    Bronisław Knaster: (with K. Kuratowski) Problème 2, Fundamenta Mathematicae 1 (1920), 223.Google Scholar
  79. [K79]
    Bronisław Knaster: (with K. Kuratowski) Problème 15, Fundamenta Mathematicae 2 (1921), 286.Google Scholar
  80. [K80]
    Bronisław Knaster: (with K. Zarankiewicz) Problème 42, Fundamenta Mathematicae 8 ( 1926, 376.Google Scholar
  81. [K81]
    Bronisław Knaster: Problème 43, Fundamenta Mathematicae 8 (1926), 376.Google Scholar
  82. [K82]
    Bronisław Knaster: Problème P 4, Colloquium Mathematicum 1 (1948), 30–31.Google Scholar
  83. [K83]
    Bronisław Knaster: Problème P 65, Colloquium Mathematicum 2 (1951), 60. [K841 Problème P 100, Colloquium Mathematicum 2 (1951), 301.Google Scholar
  84. [K85]
    Bronisław Knaster: Problème P 123, Colloquium Mathematicum 3 (1955), 74.Google Scholar
  85. [K86]
    Bronisław Knaster: with J. Mioduszewski and K. Urbanik) Problème P 132, Colloquium Mathematicum 3 (1955), 170.Google Scholar
  86. [K87]
    Bronisław Knaster: Problèmes P 148 et 149, Colloquium Mathematicum 4 (1957), 89–90.Google Scholar
  87. [K88]
    Bronisław Knaster: Problèmes P 177 et 178, Colloquium Mathematicum 4 (1957), 243.Google Scholar
  88. [K89]
    Bronisław Knaster: Problème P 195, Colloquium Mathematicum 5 (1958), 117.Google Scholar
  89. [K90]
    Bronisław Knaster: Problèmes P 201 - P 204, Colloquium Mathematicum 5 (1958), 118.Google Scholar
  90. [K91]
    Bronisław Knaster: Problèmes P 222 - P 224, Colloquium Mathematicum 5 (1958), 234–235.Google Scholar
  91. [K92]
    Bronisław Knaster: Problème P 253, Colloquium Mathematicum 6 (1958), 332.Google Scholar
  92. [K93]
    Bronisław Knaster: Problèmes P 264 - P 266, Colloquium Mathematicum 6 (1958), 334–335.Google Scholar
  93. [K94]
    Bronisław Knaster: (with A. Lelek) Problème P 267, Colloquium Mathematicum 6 (1958), 335.Google Scholar
  94. [K95]
    Bronisław Knaster: (with A. Lelek)Problème P 281, Colloquium Mathematicum 7 (1960), 108.Google Scholar
  95. [K96]
    Problème P 284, Colloquium Mathematicum 7 (1960), 108.Google Scholar
  96. [K97]
    Bronisław Knaster: (with A. Lelek) Problème P 290, Colloquium Mathematicum 7 (1960), 110.Google Scholar
  97. [K98]
    Bronisław Knaster: Problème P 304, Colloquium Mathematicum 7 (1960), 310.Google Scholar
  98. [K99]
    Bronisław Knaster: Problèmes P 323 et P 324, Colloquium Mathematicum 8 (1961), 139.Google Scholar
  99. [K100]
    Bronisław Knaster: Problème P 340, Colloquium Mathematicum 8 (1961), 278.Google Scholar
  100. [K101]
    Bronisław Knaster: Exercise 322, Matematyka 3(25) (1953), 54 and 6 (34) (1954), 109. [in Polish]Google Scholar
  101. [K102]
    Bronisław Knaster: Problème P 370, Colloquium Mathematicum 9 (1962), 169.Google Scholar
  102. [K103]
    Bronisław Knaster: Problèmes P 480 et P 481, Colloquium Mathematicum 12 (1964), 294–295.Google Scholar
  103. [K104]
    Bronisław Knaster: Problème P 554, Colloquium Mathematicum 15 (1966), 160.Google Scholar
  104. [K105]
    Bronisław Knaster: Problème P 562, Colloquium Mathematicum 15 (1966), 320.Google Scholar
  105. [K106]
    Bronisław Knaster: Problème P 683, Colloquium Mathematicum 21 (1970), 163.Google Scholar
  106. [K107]
    Bronisław Knaster: Problème P 737, Colloquium Mathematicum 23 (1971), 178–179.Google Scholar
  107. [K108]
    Bronisław Knaster: Problème P 846, Colloquium Mathematicum 27 (1973), 332.Google Scholar
  108. [K109]
    Bronisław Knaster: Problème P 1138, Colloquium Mathematicum 42 (1979), 396.Google Scholar
  109. [K110]
    Bronisław Knaster: Problem 69 in: Continua, with the Houston problem book, H. Cook, W. T. Ingram, K. T. Kuperberg, A. Lelek and P. Minc (editors), M. Dekker 1995; p. 378.Google Scholar
  110. [K111]
    Bronisław Knaster: Problem 126 in: Continua, with the Houston problem book, H. Cook, W. T. Ingram, K. T. Kuperberg, A. Lelek and P. Mine (editors), M. Dekker 1995; p. 385.Google Scholar

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Copyright information

© Springer Science+Business Media Dordrecht 1997

Authors and Affiliations

  • Janusz J. Charatonik
    • 1
  1. 1.Mathematical InstituteUniversity of WrocławWrocławPoland

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