Abstract
In Parts II to IV, we are going to investigate simultaneous extensions of various topological structures (i.e. traces on several subsets at the same time are prescribed), also with separation axioms T0, T1, symmetry (in the sense of Part I, § 3), Riesz property, Lodato property. The following questions will be considered: (i) Under what conditions is there an extension? (ii) How can the finest extension be described? (iii) Is there a coarsest extension? (iv) Can we say more about extensions of two structures than in the general case? (v) Assume that certain subfamilies (e.g. the finite ones) can be extended; does the whole family have an extension, too? The general categorial results from Part I will be applied whenever possible (even when they are not really needed).
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References
J. Adámek, H. Herrlich andG. E. Strecker,Abstract and concrete categories, Wiley, New York, 1990.
Á. Császár andJ. Deák, Simultaneous extensions of proximities, semi-uniformities, contiguities and merotopies I–IV,Math. Pannon. 1 (1990) No. 2, 67–90;2 (1991) No. 1, 19–35;2 (1991) No. 2, 3–23;3 (1992) No. 1, 57–76.
G. Preuss,Theory of topological structures, D. Reidel, Dordecht, 1988.
S. Weck-Schwarz, T0-objects and separated objects in topological categories,Quaestiones Math. 14 (1991) No. 3, 315–325.
E. Čech,Topological spaces, Academia, Prague, 1966.MR 35#2254.
Á. Császár, Proximities, screens, merotopies, uniformities I–IV,Acta Math. Hungar. 49 (1987), No. 3–4, 459–479;50 (1987) No. 1–2, 97–109;51 (1988) No. 1–2, 23–33;51 (1988) No. 1–2, 151–164.MR 88k:54002ab;89e:54019ab.
Á. Császár, Simultaneous extensions of screens,Topology, theory and applications II, Colloq. Math. Soc. J. Bolyai55, North-Holland, Amsterdam, 1993, 107–126.
Á. Császár, Simultaneous extensions of Cauchy structures,Acta Math. Hungar.
M. S. Hastings, On hemi-nearness spaces,Proc. Amer. Math. Soc. 86 (1982) No. 4, 567–573.MR 84c:54047.
H. Herrlich, Topological structures,Topological structures, Math. Centre Tracts52, Mathematisch Centrum, Amsterdam, 1974, 59–122.MR 50#11165.
D. Leseberg, Neighbourhood structures,Topology, Vol. I, Colloq. Math. Soc. J. Bolyai23, North-Holland, Amsterdam, 1980, 751–804.MR 82b:54018.
E. Lowen-Colebunders,Function classes of Cauchy continuous maps, Pure and Applied Mathematics123, Marcel Dekker, New York, 1989.MR 91c:54002.
E. Makai, jr., Automorphisms and full embeddings of categories in algebra and topology,Category theory at work, Heldermann, Berlin, 1991, 217–260.
W. J. Thron, What results are valid on closure spaces,Topology Proc. 6, (1981), No. 1, 135–158.MR 83e:54002.
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Research supported by Hungarian National Foundation for Scientific Research, grant no. 2114.
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Deák, J. Spaces from pieces II. Period Math Hung 29, 1–25 (1994). https://doi.org/10.1007/BF01876200
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DOI: https://doi.org/10.1007/BF01876200