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EXTENSION OF CONTINUOUS MAPPINGS AND H1-RETRACTS

Part of: Maps and general types of spaces defined by maps

Published online by Cambridge University Press:  01 December 2008

OLENA KARLOVA
OLENA KARLOVA*
Affiliation:
Department of Mathematical Analysis, Chernivtsi National University, Kotsjubyns’koho 2, Chernivtsi 58012, Ukraine (email: mathan@ukr.net)
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Abstract

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We prove that any continuous mapping f:E→Y on a completely metrizable subspace E of a perfect paracompact space X can be extended to a Lebesgue class one mapping g:X→Y (that is, for every open set V in Y the preimage g−1(V ) is an Fσ-set in X) with values in an arbitrary topological space Y.

Keywords

extensionLebesgue class one mappingcontinuous function

MSC classification

Secondary: 54C20: Extension of maps 54C05: Continuous maps
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 78 , Issue 3 , December 2008 , pp. 497 - 506
Copyright
Copyright © 2009 Australian Mathematical Society

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