Naslov
An existence theorem concerning strong shape of Cartesian products

Autori
Mardešić, Sibe

Izvornik
Mathematical communications (1331-0623) 17 (2012), 2; 313-354

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

Ključne riječi
shape ; strong shape ; direct product ; Cartesian prodsuct ; inverse limit. resolution ; cpherent homotopy

Sažetak
The paper is devoted to the question is the Cartesian product $X\times P$ of a compact Hausdorff space $X$ and a polyhedron $P$ a product in the strong shape category SSh of topological spaces. The question consists of two parts. The existence part, which asks whether, for a topological space $Z$, for a strong shape morphism $F\colon Z\to X$ and a homotopy class of mappings $[g]\colon Z\to P$, there exists a strong shape morphism $H\colon Z\to X\times P$, whose compositions with the canonical projections of $X\times P$ equal $F$ and $[g]$, respectively. The uniqueness part asks if $H$ is unique. The main result of the paper asserts that $H$ exists, whenever $Z$ is either metrizable or has the homotopy type of a polyhedron. If $X$ is a metric compactum, $H$ exists for all topological spaces $Z$. The proofs use resolutions of spaces and coherent homotopies of inverse systems. It is known that, in the ordinary shape category Sh, $H$ need not be unique, even in the case when $Z$ is a metrizable space or a polyhedron.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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