Naslov
An existence theorem concerning ordinary shape of Cartesian products

Autori
Mardešić, Sibe

Izvornik
Matematički bilten (0351-336X) 35 (2011); 5-13

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

Ključne riječi
shape ; ordinary shape ; strong shape ; direct product ; Cartesian product ; resolution ; homotopy mapping of systems ; inverse limit ; coherent homotopy

Sažetak
The paper is devoted to the question when is the Cartesian product X × P of a compact metric space X and a polyhedron P a product in the shape category of topological spaces. The question consists of two parts. The existence part, which asks whether, for every topological space Z, every shape morphism F : Z → X and every homotopy class of mappings [g] : Z → P, there exists a shape morphism H : Z → X × P, whose compositions with the canonical projections of X × P equal F and [g], respectively. The uniqueness part asks whether H is unique. It is known that, in general, the uniqueness part does not hold even when Z is a polyhedron. The main result of the paper asserts that the existence part always holds. The proof is based on an analogous result for strong shape.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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