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SOME WEAKER FORMS OF THE CHAIN (F) CONDITION FOR METACOMPACTNESS

Part of: Fairly general properties

Published online by Cambridge University Press:  01 April 2008

ÇETIN VURAL
ÇETIN VURAL*
Affiliation:
Gazi Universitesi, Fen-Edebiyat Fakultesi Matematik Bolumu, 06500 Teknikokullar, Ankara, Turkey (email: cvural@gazi.edu.tr)
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Abstract

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We define, in a slightly unusual way, the rank of a partially ordered set. Then we prove that if X is a topological space and satisfies condition (F) and, for every x∈X, is of the form , where is Noetherian of finite rank, and every other is a chain (with respect to inclusion) of neighbourhoods of x, then X is metacompact. We also obtain a cardinal extension of the above. In addition, we give a new proof of the theorem ‘if the space X has a base of point-finite rank, then X is metacompact’, which was proved by Gruenhage and Nyikos.

Keywords

point-countablemetacompactrankNoetherianrefinement

MSC classification

Secondary: 54D20: Noncompact covering properties (paracompact, Lindelöf, etc.)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 84 , Issue 2 , April 2008 , pp. 283 - 288
Copyright
Copyright © 2008 Australian Mathematical Society

References

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