Spaces of countable and point-countable type

Vaughan, J. E.

doi:10.1090/S0002-9947-1970-0266157-6

Spaces of countable and point-countable type
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by J. E. Vaughan PDF

Trans. Amer. Math. Soc. 151 (1970), 341-351 Request permission

Abstract:

These spaces were introduced by M. Henriksen and J. R. Isbell, and A. V. Arhangel’skiĭ, who proved results about the placement of such spaces in their compactifications. In the present paper, these results are consolidated using new terminology. In addition, further results concerning the heredity of these spaces are obtained. Generalizations of these spaces are introduced, and an analogous treatment is given for them. Finally, some examples are given of which one gives a solution to a problem raised by Arhangel’skiĭ by showing that the perfect image of a first countable space need not be of point-countable type.

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