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PRODUCTS OF BASE-κ-PARACOMPACT SPACES AND COMPACT SPACES

Part of: Fairly general properties Basic constructions

Published online by Cambridge University Press:  21 July 2011

LEI MOU
LEI MOU*
Affiliation:
Mathematics Department, Capital Normal University, Beijing 100048, PR China (email: [email protected])
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Abstract

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Let λ be a regular ordinal with λ≥ω1. Then we prove that (λ+1)×λ is not base-countably metacompact. This implies that base-κ-paracompactness is not an inverse invariant of perfect mappings, which answers a question asked by Yamazaki.

Keywords

baseparacompactproductordinal

MSC classification

Secondary: 54B10: Product spaces 54D70: Base properties
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 84 , Issue 3 , December 2011 , pp. 387 - 392
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

References

[1]Gruenhage, G., ‘Base-paracompactness and base-normality of GO-spaces’, Questions Answers Gen. Topology 23 (2005), 137–141.Google Scholar
[2]Kemoto, N., Ohta, H. and Tamano, K., ‘Products of spaces of ordinal numbers’, Topology Appl. 45 (1992), 245–260.CrossRefGoogle Scholar
[3]Kemoto, N. and Smith, K. D., ‘Hereditary countable metacompactness in finite and infinite product spaces of ordinals’, Topology Appl. 77 (1997), 57–63.CrossRefGoogle Scholar
[4]Kunen, K., Set Theory. An Introduction to Independence Proofs (North-Holland, Amsterdam, 1980).Google Scholar
[5]Morita, K., ‘Paracompactness and product spaces’, Fund. Math. 50 (1961/62), 223–236.CrossRefGoogle Scholar
[6]Mou, L., ‘Base-normality and total paracompactness of subspaces of products of two ordinals’, Sci. Math. Jpn. 63 (2006), 89–100.Google Scholar
[7]Mou, L., Wang, R. and Wang, S., ‘Base metacompact spaces’, Adv. Math. 40 (2011), 111–117.Google Scholar
[8]Porter, J. E., ‘Base-paracompact spaces’, Topology Appl. 128 (2003), 145–156.CrossRefGoogle Scholar
[9]Yamazaki, K., ‘Base-normality and product spaces’, Topology Appl. 148 (2005), 123–142.CrossRefGoogle Scholar