Napredna pretraga

## The Cartesian product of a compactum and a space is a bifunctor in shape

Mardešić, Sibe
The Cartesian product of a compactum and a space is a bifunctor in shape // Topology and its applications, 156 (2009), 14; 2326-2345 doi:10.1016/j.topol.2009.05.014 (međunarodna recenzija, članak, znanstveni)

CROSBI ID: 431636 Za ispravke kontaktirajte CROSBI podršku putem web obrasca

Naslov
The Cartesian product of a compactum and a space is a bifunctor in shape

Autori
Mardešić, Sibe

Izvornik
Topology and its applications (0166-8641) 156 (2009), 14; 2326-2345

Ključne riječi
Inverse system; inverse limit; resolution; coherent mapping; Cartesian product; shape; strong shape; simplicial mapping; bifunctor.

Sažetak
In 2003 the author has associated with every cofinite inverse system of compact Hausdorff space <b>X</b> with limit <i>X</i> and every simplicial complex <i>K</i> (possibly infinite) with geometric realization <i>P</i>=|<i>K</i>| a resolution R(<b>X</b>, <i>K</i>) of <i>X</i>×<i>P</i>, which consists of paracompact spaces. If <b>X</b> consists of compact polyhedra, then R(<b>X</b>, <i>K</i>) consists of spaces having the homotopy type of polyhedra. In two subsequent papers the author proved that R(<b>X</b>, <i>K</i>) is a covariant functor in each of its variables <b>X</b> and <i>K</i>. In the present paper it is proved that R(<b>X</b>, <i>K</i>) is also a covariant functor in the variable <i>K</i>. Moreover, R(<b>X</b>, <i>K</i>) is a bifunctor. This implies that the Cartesian product <i>X</i>×<i>P</i> is a bifunctor SSh(Cpt)×</>Sh(Top)→</>Sh(Top) from the product category SSh(Cpt)×</>H(Pol) of the strong shape category of compact Hausdorff spaces SSh(Cpt) and the homotopy category H(Pol) of polyhedra to the shape category Sh(Top) of topological spaces. This holds in spite of the fact that <i>X</i>×<i>Z</i> need not be a direct product in Sh(Top).

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
The Cartesian product of a compactum and a space is a bifunctor in shape // Topology and its applications, 156 (2009), 14; 2326-2345 doi:10.1016/j.topol.2009.05.014 (međunarodna recenzija, članak, znanstveni)
Mardešić, S. (2009) The Cartesian product of a compactum and a space is a bifunctor in shape. Topology and its applications, 156 (14), 2326-2345 doi:10.1016/j.topol.2009.05.014.
@article{article, author = {Marde\v{s}i\'{c}, S.}, year = {2009}, pages = {2326-2345}, DOI = {10.1016/j.topol.2009.05.014}, keywords = {Inverse system, inverse limit, resolution, coherent mapping, Cartesian product, shape, strong shape, simplicial mapping, bifunctor.}, journal = {Topology and its applications}, doi = {10.1016/j.topol.2009.05.014}, volume = {156}, number = {14}, issn = {0166-8641}, title = {The Cartesian product of a compactum and a space is a bifunctor in shape}, keyword = {Inverse system, inverse limit, resolution, coherent mapping, Cartesian product, shape, strong shape, simplicial mapping, bifunctor.} }

#### Časopis indeksira:

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

#### Uključenost u ostale bibliografske baze podataka:

• Mathematical Reviews
• Zentralblatt fur Mathematik

#### Citati

Contrast
Increase Font
Decrease Font
Dyslexic Font