Vol. 36, No. 1, 1971

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 294: 1
Vol. 293: 1  2
Vol. 292: 1  2
Vol. 291: 1  2
Vol. 290: 1  2
Vol. 289: 1  2
Vol. 288: 1  2
Vol. 287: 1  2
Online Archive
The Journal
Editorial Board
Special Issues
Submission Guidelines
Submission Form
Author Index
To Appear
ISSN: 0030-8730
Conditions for countable bases in spaces of countable and point-countable type

David Michael Henry

Vol. 36 (1971), No. 1, 181–183

A space X is of countable type if for every compact C X, there exists a compact set K having a countable basis with C K.X is of point-countable type if there exists a covering of compact subsets of X, each having a countable basis. It is shown that in a Hausdorff space of countable type, a compact set has a countable basis if and only if it is a Gδ-set. Similarly, for Hausdorff spaces of point-countable type, a point has a countable basis if and only if it is a Gδ-set.

Mathematical Subject Classification
Primary: 54.40
Received: 4 May 1970
Revised: 26 June 1970
Published: 1 January 1971
David Michael Henry