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

The induced homology and homotopy functors on the coarse shape category (CROSBI ID 161210)

Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija

Koceić-Bilan, Nikola The induced homology and homotopy functors on the coarse shape category // Glasnik matematički, 45 (2010), 2; 531-557

Podaci o odgovornosti

Koceić-Bilan, Nikola

engleski

The induced homology and homotopy functors on the coarse shape category

In this paper we consider some algebraic invariants of the coarse shape. We introduce functors pro*-H-n and pro*-pi(n) relating the (pointed) coarse shape category (Sh(star)*) Sh* to the category pro*- Grp. The category (Sh(star)*) Sh*, which is recently constructed, is the supercategory of the (pointed) shape category (Sh(star)) Sh*, having all (pointed) topological spaces as objects. The category pro*-Grp is the supercategory of the category of pro-groups pro-Grp, both having the same object class. The functors pro*-H-n and pro*-pi(n) extend standard functors pro-H-n and pro-pi(n) which operate on (Sh(star)) Sh*. The full analogue of the well known Hurewicz theorem holds also in Sh(star)*. We proved that the pro-homology (homotopy) sequence of every pair (X, A) of topological spaces, where A is normally embedded in X, is also exact in pro*-Grp. Regarding this matter the following general result is obtained: for every category C with zero-objects and kernels, the category pro-C is also a category with zero-objects and kernels, while morphisms of pro*-C generally don't have kernels.

topological space ; polyhedron ; inverse system ; pro-category ; pro*-category ; expansion ; shape ; coarse shape ; homotopy pro-group ; homology pro-group ; n-shape connectedness ; kernel ; exact sequence

nije evidentirano

nije evidentirano

nije evidentirano

nije evidentirano

nije evidentirano

nije evidentirano

Podaci o izdanju

45 (2)

2010.

531-557

objavljeno

0017-095X

1846-7989

Povezanost rada

Matematika

Indeksiranost