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Concerning collectionwise Hausdorff spaces

  • James R. Boone (a1)

Abstract

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.

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References

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[1]Boone, James R., “Some characterizations of paracompactness in k–spaces”, Fund. Math. 72 (1971), 145153.
[2]Boone, James R., “A metrization theorem for developable spaces”, Fund. Math. 73 (1971), 7983.
[3]Boone, James R., “A characterization of metacompactness in the class of θ-refinable spaces”, General Topology and Appl. 3 (1973), 253264.
[4]Christian, U.J., “Concerning certain minimal cover refinable spaces”, Fund. Math. 76 (1972), 213222.
[5]Fitzpatrick, Ben Jr., “On dense subspaces of Moore spaces II”, Fund. Math. 61 (1967), 9192.
[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.
[7]Tall, Franklin D., “On the existence of normal metacompact Moore spaces which are not metrizable”, Canad. J. Math. 26 (1974), 16.
[8]Worrell, J.M. Jr., and Wicke, H.H., “Characterizations of developable topological spaces”, Canad. J. Math. 17 (1965), 820830.
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Concerning collectionwise Hausdorff spaces

  • James R. Boone (a1)

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