Naslov
Images of ANR’s under shape fibrations

Autori
Coram, Donald S. ; Mardešić, Sibe ; Torunczyk, Henryk

Izvornik
Bulletin of the Polish Academy of Sciences. Mathematics (0239-7269) 33 (1985); 181-187

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
hereditary shape equivalence onto a metric compactum ; ANR ; cell-like map ; maps with point-inverses which have non-trivial shape ; shape fibrations ; shape dominations ; approximate right inverses

Sažetak
G. Kozlowski proved that if X is a compact ANR and f:X→Y is a hereditary shape equivalence onto a metric compactum Y, then Y is also an ANR. Note that a hereditary shape equivalence is a cell-like map ; that is, its point-inverses have trivial shape. This paper establishes a result analogous to Kozlowski’s theorem for maps with point-inverses which have non-trivial shape. In particular, it is shown that images of compact ANR’s under maps which are shape fibrations and shape dominations are ANR’s. The proof involves showing that an LC∞ image of an ANR is an ANR provided that the map admits approximate right inverses

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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