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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 id 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


Puni tekst: engleski pdf 123 Kb

str. 431-439

preuzimanja: 383

citiraj


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: 878 *