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## An existence theorem concerning strong shape of Cartesian products

Mardešić, Sibe
An existence theorem concerning strong shape of Cartesian products // Mathematical Communications, 17 (2012), 313-354 (međunarodna recenzija, članak, znanstveni)

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Naslov
An existence theorem concerning strong shape of Cartesian products

Autori
Mardešić, Sibe

Izvornik
Mathematical Communications (1331-0623) 17 (2012); 313-354

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

Projekt / tema
037-0372791-2802 - Teorija dimenzije i oblika (Sibe Mardešić, )

Ustanove
Prirodoslovno-matematički fakultet, Matematički odjel, Zagreb

Profili:

Sibe Mardešić (autor)

#### Citiraj ovu publikaciju

Mardešić, Sibe
An existence theorem concerning strong shape of Cartesian products // Mathematical Communications, 17 (2012), 313-354 (međunarodna recenzija, članak, znanstveni)
Mardešić, S. (2012) An existence theorem concerning strong shape of Cartesian products. Mathematical Communications, 17, 313-354.
@article{article, author = {Marde\v{s}i\'{c}, S.}, year = {2012}, pages = {313-354}, keywords = {shape, strong shape, direct product, Cartesian prodsuct, inverse limit. resolution, cpherent homotopy}, journal = {Mathematical Communications}, volume = {17}, issn = {1331-0623}, title = {An existence theorem concerning strong shape of Cartesian products}, keyword = {shape, strong shape, direct product, Cartesian prodsuct, inverse limit. resolution, cpherent homotopy} }

#### Časopis indeksira:

• Web of Science Core Collection (WoSCC)
• Science Citation Index Expanded (SCI-EXP)
• SCI-EXP, SSCI i/ili A&HCI
• Scopus

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