Vol. 47, No. 1, 1973

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
Volume:
Issue:
     
The Journal
Subscriptions
Editorial Board
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
Author Index
To Appear
 
ISSN: 0030-8730
Axioms of countability and the algebra C(X)

William Alan Feldman

Vol. 47 (1973), No. 1, 81–89
Abstract

Relationships between a topological space (more generally a convergence space) and its associated function space C(X) are investigated. The algebra of all continuous real-valued functions on a space X together with the continuous convergence structure is denoted by Cc(X). After appropriate generalizations of the axioms of countability to convergence spaces, it is shown: 1. A completely regular topological space X is Lindelöf if and only if Cc(X) is first countable. 2. A completely regular topological space X is separable and metrizable if and only if Cc(X) is second countable. Generalizations of (1) and (2) are introduced, and results and examples which justify the use of axioms of countability in convergence space theory are presented.

Mathematical Subject Classification 2000
Primary: 54C35
Milestones
Received: 7 March 1972
Published: 1 July 1973
Authors
William Alan Feldman