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Concerning collectionwise Hausdorff spaces

Published online by Cambridge University Press:  17 April 2009

James R. Boone
James R. Boone
Affiliation:
Department of Mathematics, Texas A&M University, College Station, Texas, USA.
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Abstract

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In this paper the notion of a space which has property (ω) pointwise is studied. The primary application of this concept is a reformulation of Tall's existence theorem for normal non-metrizable metacompact Moore spaces in terms of families which are finite on convergent sequences. Since the first countability in Tall's theorem yields an abundance of convergent sequences, this reformulation places the existence theorem in a natural setting.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 11 , Issue 2 , October 1974 , pp. 255 - 261
Copyright
Copyright © Australian Mathematical Society 1974

References

[1]Boone, James R., “Some characterizations of paracompactness in k–spaces”, Fund. Math. 72 (1971), 145–153.CrossRefGoogle Scholar
[2]Boone, James R., “A metrization theorem for developable spaces”, Fund. Math. 73 (1971), 79–83.CrossRefGoogle Scholar
[3]Boone, James R., “A characterization of metacompactness in the class of θ-refinable spaces”, General Topology and Appl. 3 (1973), 253–264.CrossRefGoogle Scholar
[4]Christian, U.J., “Concerning certain minimal cover refinable spaces”, Fund. Math. 76 (1972), 213–222.CrossRefGoogle Scholar
[5]Fitzpatrick, Ben Jr., “On dense subspaces of Moore spaces II”, Fund. Math. 61 (1967), 91–92.CrossRefGoogle Scholar
[6]Tall, Franklin D., “Set-theoretic consistency results and topological theorems concerning the normal Moore space conjecture and related problems”, PhD thesis, University of Wisconsin, Madison, 1969.Google Scholar
[7]Tall, Franklin D., “On the existence of normal metacompact Moore spaces which are not metrizable”, Canad. J. Math. 26 (1974), 1–6.CrossRefGoogle Scholar
[8]Worrell, J.M. Jr., and Wicke, H.H., “Characterizations of developable topological spaces”, Canad. J. Math. 17 (1965), 820–830.CrossRefGoogle Scholar