Nalazite se na CroRIS probnoj okolini. Ovdje evidentirani podaci neće biti pohranjeni u Informacijskom sustavu znanosti RH. Ako je ovo greška, CroRIS produkcijskoj okolini moguće je pristupi putem poveznice www.croris.hr
izvor podataka: crosbi

An existence theorem concerning strong shape of Cartesian products (CROSBI ID 190771)

Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija

Mardešić, Sibe An existence theorem concerning strong shape of Cartesian products // Mathematical communications, 17 (2012), 2; 313-354

Podaci o odgovornosti

Mardešić, Sibe

engleski

An existence theorem concerning strong shape of Cartesian products

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.

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

nije evidentirano

nije evidentirano

nije evidentirano

nije evidentirano

nije evidentirano

nije evidentirano

Podaci o izdanju

17 (2)

2012.

313-354

objavljeno

1331-0623

1848-8013

Povezanost rada

Matematika

Poveznice
Indeksiranost