Coherent and strong expansions of spaces coincide

• Autorzy: Sibe Mardešić
• 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.

Słowa kluczowe

EN

coherent expansion; coherent homotopy; inverse system; strong expansion; strong shape

Kategorie tematyczne

• 55P55: Shape theory
• 54B35: Spectra
• 55U35: Abstract and axiomatic homotopy theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1998
• Tom: 158
• Numer: 1
• Strony: 69-80

Daty

wydano

1998

otrzymano

1997-10-01

Twórcy

autor

Sibe Mardešić

• Department of Mathematics, University of Zagreb, Bijenička cesta 30, 10.000 Zagreb, Croatia

Bibliografia

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• [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.
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