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A Characterization of Spaces Having Bases of Countable Order in Terms of Primitive Bases

Published online by Cambridge University Press:  20 November 2018

H. H. Wicke  and
J. M. Worrell Jr.
H. H. Wicke
Affiliation:
Ohio University, Athens, Ohio
J. M. Worrell Jr.
Affiliation:
Ohio University, Athens, Ohio
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The main theorem of this paper characterizes the class of essentially T1 spaces having bases of countable order as those spaces of the class of essentially T1 spaces having primitive bases in which closed sets are sets of interior condensation. In addition we deduce some corollaries of this theorem, derive some other characterizations, and prove a lemma concerning primitive sequences which is a key to the proof of the main theorem and has other applications.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 27 , Issue 5 , 01 October 1975 , pp. 1100 - 1109
Copyright
Copyright © Canadian Mathematical Society 1975

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