Glasnik matematički, Vol. 47 No. 2, 2012.
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
Datum izdavanja:
19.12.2012.
Posjeta: 933 *