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1998 | 158 | 1 | 69-80
Tytuł artykułu

Coherent and strong expansions of spaces coincide

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Języki publikacji
EN
Abstrakty
EN
In the existing literature there are several constructions of the strong shape category of topological spaces. In the one due to Yu. T. Lisitsa and S. Mardešić [LM1-3] an essential role is played by coherent polyhedral (ANR) expansions of spaces. Such expansions always exist, because every space admits a polyhedral resolution, resolutions are strong expansions and strong expansions are always coherent. The purpose of this paper is to prove that conversely, every coherent polyhedral (ANR) expansion is a strong expansion. This result is obtained by showing that a mapping of a space into a system, which is coherently dominated by a strong expansion, is itself a strong expansion.
Rocznik
Tom
158
Numer
1
Strony
69-80
Opis fizyczny
Daty
wydano
1998
otrzymano
1997-10-01
Twórcy
  • Department of Mathematics, University of Zagreb, Bijenička cesta 30, 10.000 Zagreb, Croatia, smardes@math.hr
Bibliografia
  • [G] B. Günther, Comparison of the coherent pro-homotopy theories of Edwards-Hastings, Lisica-Mardešić and Günther, Glas. Mat. 26 (1991), 141-176.
  • [LM1] Ju. T. Lisica and S. Mardešić, Steenrod-Sitnikov homology for arbitrary spaces, Bull. Amer. Math. Soc. 9 (1983), 207-210.
  • [LM2] Ju. T. Lisica and S. Mardešić, Coherent prohomotopy and strong shape category of topological spaces, in: Proc. Internat. Topology Conference (Leningrad, 1982), Lecture Notes in Math. 1060, Springer, Berlin, 1984, 164-173.
  • [LM3] Ju. T. Lisica and S. Mardešić, Coherent prohomotopy and strong shape theory, Glas. Mat. 19 (39) (1984), 335-399.
  • [M1] S. Mardešić, Approximate polyhedra, resolutions of maps and shape fibrations, Fund. Math. 114 (1981), 53-78.
  • [M2] S. Mardešić, Strong expansions and strong shape theory, Topology Appl. 38 (1991), 275-291.
  • [M3] S. Mardešić, Resolutions of spaces are strong expansions, Publ. Inst. Math. Beograd 49 (63) (1991), 179-188.
  • [M4] S. Mardešić, Strong expansions and strong shape for pairs of spaces, Rad Hrvat. Akad. Znan. Umjetn. Matem. Znan. 456 (10) (1991), 159-172.
  • [M5] S. Mardešić, Coherent homotopy and localization, Topology Appl. (1998) (to appear).
  • [MS] S. Mardešić and J. Segal, Shape Theory - The Inverse System Approach, North-Holland, Amsterdam, 1982.
  • [T] H. Thiemann, Strong shape and fibrations, Glas. Mat. 30 (1995), 135-174.
  • [V] R. M. Vogt, A note on homotopy equivalences, Proc. Amer. Math. Soc. 32 (1972), 627-629.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-fmv158i1p69bwm
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