Naslov
The coarse shape and its invariants

Autori
Koceić Bilan, Nikola

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni

Izvornik
Book of abstracts, Massee, International Congress on Mathematics MIOCOM 2009 / - Ohrid, 2009, 17-17

Skup
International Congress on Mathematics MIOCOM 2009

Mjesto i datum
Sjeverna Makedonija, 16.09.2009. - 20.09.2009

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
topological space; polyhedron; inverse system; pro-category; pro^{;∗};-category; shape; coarse shape; shape group; coarse shape group

Sažetak
In 1976, K. Borsuk, for the very first time, has presented some relations between metric compacta coarser then a shape, but it has been proved in <cite>KKU</cite> that Borsuk's relation of quasi-equivalence is not transitive. However, this idea of space classifications, coarser then a shape type, plays an important role in topology. Namely, such classifications could provide some informations about spaces having different shape type which standard shape theory is not able to give. Recently, coarse shape category Sh^{;∗}; whose objects are all topological spaces is constructed (<cite>KU</cite>). Isomorphisms of Sh^{;∗}; classify topological spaces strictly coarser than the shape does, but the coarse shape, shape and homotopy type classification coincide on the class of polyhedra. Since the shape category Sh can be considered as the subcategory of Sh^{;∗}; one may say that the coarse shape generalizes shape theory. The coarse shape, similar to shape, uses a technique of inverse systems, but essentially they both differ (<cite>KB</cite>). All fibres of shape fibration over an arbitrary metric continuum, generally, don't have the same shape type, but they are mutually coarse shape equivalent. The coarse shape preserves some important topological invariants as connectedness, (strong) movability, shape dimension and stability. There are also several new algebraic coarse shape invariants e.g. coarse shape groups π_{;n};^{;∗};(X, ∗).

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA