Abstract
A continuum is constructed that is not coarse-shape-path connected. This implies that the coarse-shape theory is strictly finer (at least for bi-pointed continua) than the weak-shape theory.
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Borsuk, K.: Theory of Shape, Monografie Matematyczne, Vol. 59. Polish Scientific Publishers, Warszawa (1975)
Keesling J., Mardešić S.: A shape fibration with fibers of different shape. Pacific J. Math. 84, 319–331 (1979)
Koceić Bilan N., Uglešić N.: The coarse shape. Glasnik. Mat. 42(62), 145–187 (2007)
Koceić Bilan N., Uglešić N.: The coarse shape path connectedness. Glasnik Mat. 46(66), 489–503 (2011)
Krasinkiewicz J., Minc, P.: Generalized paths and pointed 1-movability. Fund. Math 104, 141–153 (1979)
Mardešić, S., Segal, J.: Shape Theory. North-Holland, Amsterdam (1982)
Mardešić S., Uglešić N.: A category whose isomorphisms induce an equivalence relation coarser than shape. Top. Appl. 153, 448–463 (2005)
Uglešić N.: Continuity in the coarse and weak shape categories. Mediter. J. Math. 9, 741–766 (2012)
Uglešić N., Červar, B..: The concept of a weak shape type. Int. J. Pure Appl. Math. 39, 363–428 (2007)
Ungar, Š.: A remark on shape paths and homotopy pro-groups. General topology and its relations to modern analysis and algebra V. In: Proceedings of 5th Prague Topology Symposium on, 1981, pp. 642–647, (J. Nowak, ed.), Heldermann-Verlag, Berlin (1982)
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Uglešić, N. An Example Relating the Coarse and Weak Shape. Mediterr. J. Math. 13, 4939–4947 (2016). https://doi.org/10.1007/s00009-016-0784-7
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DOI: https://doi.org/10.1007/s00009-016-0784-7