Glasnik Matematicki, Vol. 47, No. 2 (2012), 431-439.

MAP OF QUASICOMPONENTS INDUCED BY A SHAPE MORPHISM

Nikita Shekutkovski, Tatjana Atanasova-Pachemska and Gjorgji Markoski

University "Goce Delchev" - Shtip, Faculty of Informatics, 2000 Shtip, Republic of Macedonia
e-mail: tatjana.pacemska@ugd.edu.mk

Institute of Mathematics, Faculty of Natural Sciences and Mathematics, Sts. Cyril and Methodius University, 1000 Skopje, Republic of Macedonia
e-mail: gorgim@pmf.ukim.mk

Abstract.   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.

2010 Mathematics Subject Classification.   54C56, 55P55, 54C08.

Key words and phrases.   Intrinsic definition, continuity up to a covering, proximate sequence, proximate net, quasicomponents.

DOI: 10.3336/gm.47.2.16

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