Vol. 41, No. 2, 1972

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ISSN: 0030-8730
Completely adequate neighborhood systems and metrization

Sean B. O’Reilly

Vol. 41 (1972), No. 2, 513–524

In this paper, the notion of a completely adequate neighborhood system for a topological space is defined and used to obtain characterizations of discreteness and second countability. Certain conditions on the completely adequate neighborhood system are given which yield collection wise normality and paracompactness. The notion of a standardized topological space is introduced (the class of standardized spaces includes, among others, the separable spaces and the developable spaces) and the main theorem gives necessary and sufficient conditions for the metrizability of standardized spaces in terms of completely adequate neighborhood systems.

Mathematical Subject Classification 2000
Primary: 54E35
Received: 26 January 1971
Revised: 26 July 1971
Published: 1 May 1972
Sean B. O’Reilly