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Characterizations of Developable Topological Spaces

Published online by Cambridge University Press:  20 November 2018

J. M. Worrell Jr.  and
H. H. Wicke
J. M. Worrell Jr.
Affiliation:
Sandia Laboratory, Albuquerque
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The class of developable topological spaces, which includes the metrizable spaces, has been fundamentally involved in investigations in point set topology. One example is the remarkable edifice of theorems relating to these spaces constructed by R. L. Moore (13). Another is the role played by the developable property in several metrization theorems, including Alexandroff and Urysohn's original solution of the general metrization problem (1).

This paper presents an anslysis of the concept of developable space in terms of certain more extensive classes of spaces satisfying the first axiom of countability : spaces with a base of countable order and those having what is here called a θ-base. The analysis is given in the characterizations of Theorems 3 and 4 below.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 17 , 1965 , pp. 820 - 830
Copyright
Copyright © Canadian Mathematical Society 1965

References

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