Izvorni znanstveni članak

https://doi.org/10.3336/gm.47.2.16

Map of quasicomponents induced by a shape morphism

Nikita Shekutkovski ; Institute of Mathematics, Faculty of Natural Sciences and Mathematics, Sts. Cyril and Methodius University, 1000 Skopje, Republic of Macedonia
Tatjana Atanasova-Pachemska orcid.org/0000-0001-6740-9327 ; University "Goce Delchev" - Shtip, Faculty of Informatics, 2000 Shtip, Republic of Macedonia
Gjorgji Markoski ; Institute of Mathematics, Faculty of Natural Sciences and Mathematics, Sts. Cyril and Methodius University, 1000 Skopje, Republic of Macedonia

Sažetak

Using the intrinsic definition of shape we prove an analogue of well known Borsuk’s theorem for compact metric spaces. Suppose X and Y are locally compact metric spaces with compact spaces of quasicomponents QX and QY. For a shape morphism f: X → Y there exists a unique continuous map f# :QX → QY, such that for a quasicomponent Q from X and W a clopen set containing f# (Q) the restriction f:Q → W, is a shape morphism, also.

Ključne riječi

Intrinsic definition; continuity up to a covering; proximate sequence; proximate net; quasicomponents

Hrčak ID:

93959

URI

https://hrcak.srce.hr/93959

Datum izdavanja:

19.12.2012.

Posjeta: 1.218 *