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On different types of cleavability of topological spaces

Part of: Generalities Maps and general types of spaces defined by maps Spaces with richer structures

Published online by Cambridge University Press:  09 April 2009

A. V. Arhangel'skii  and
F. Cammaroto
A. V. Arhangel'skii
Affiliation:
Mech. Math. Fac. Moscow State University, Moscow, Russia
F. Cammaroto
Affiliation:
Department of Mathematics, University of Catania, Italy
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Abstract

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The notion of pointwise cleavability is introduced. We clarify those results concerning cleavability which can be or can not be generalized to the case of pointwise cleavability.

The importance of compactness in this theory is shown. Among other things we prove that t, ts, πx, the property to be Fréchet-Urysohn, radiality, biradiality, bisequentiality and so on are preserved by pointwise cleavability on the class of compact Hausdorff spaces.

Keywords

cleavabilityseparabilityMetrizabilitycompact spacestightnesscardinal invariantsFréchet-Urysohn spacespseudo radialradialsequential spacesbiradial and bisequential spacesLots.

MSC classification

Secondary: 54A20: Convergence in general topology (sequences, filters, limits, convergence spaces, etc.) 54A25: Cardinality properties (cardinal functions and inequalities, discrete subsets) 54C05: Continuous maps 54C10: Special maps on topological spaces (open, closed, perfect, etc.) 54E18: $p$-spaces, $M$-spaces, $sigma$-spaces, etc. 54E30: Moore spaces
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 58 , Issue 2 , April 1995 , pp. 183 - 199
Copyright
Copyright © Australian Mathematical Society 1995

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