Naslov
The concept of a weak shape type

Autori
Uglešić, Nikica ; Červar, Branko

Izvornik
International journal of pure and applied mathematics (1311-8080) 39 (2007), 3; 363-428

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
inverse system ; expansion ; dense subcategory ; (abstract) shape

Sažetak
For every category pair $(\mathcal{; ; ; C}; ; ; , \mathcal{; ; ; D}; ; ; )$, where $\mathcal{; ; ; D}; ; ; \subseteq\mathcal{; ; ; C}; ; ; $ is a dense and full subcategory, an (abstract) weak shape category $Sh_{; ; ; \ast(\mathcal{; ; ; C}; ; ; , \mathcal{; ; ; D}; ; ; )}; ; ; $ is constructed. There exists a faithful functor, which keeps the objects fixed, of the (abstract) shape category $Sh_{; ; ; (\mathcal{; ; ; C}; ; ; , \mathcal{; ; ; D}; ; ; )}; ; ; $ to $Sh_{; ; ; \ast(\mathcal{; ; ; C}; ; ; , \mathcal{; ; ; D}; ; ; )}; ; ; $. The main benefit is that one may expect existence of a pair of $\mathcal{; ; ; C}; ; ; $-objects (especially, topological spaces) having the same weak shape type and different shape types. Further, the weak shape type is coarser than the recently introduced coarse shape type, because there also exists a functor of the (abstract) coarse shape category $Sh_{; ; ; \mathcal{; ; ; C}; ; ; , \mathcal{; ; ; D}; ; ; )}; ; ; ^{; ; ; \ast}; ; ; $ to $Sh_{; ; ; \ast(\mathcal{; ; ; C}; ; ; , \mathcal{; ; ; D}; ; ; )}; ; ; $. It is interesting that, for metric compacta, both (coarse and weak shape) types coincide with the $S^{; ; ; \ast}; ; ; $-equivalence, which is strictly coarser than the shape type classification. An operative characterization of a weak shape isomorphism is established. Finally, it is proved that several important well known shape invariants are, actually, weak shape invariant properties.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA