Vol. 47, No. 2, 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
Mapping spaces and cs-networks

Joe Alston Guthrie

Vol. 47 (1973), No. 2, 465–471
Abstract

In this paper the space of maps from an 0-space to a space Y is studied by means of convergent sequence-networks. The notion of a cs σ-space, a simultaneous generalization of metric spaces and 0-spaces, is defined, and it is shown that if Y is a (paracompact) csσ-space then the mapping space from X to Y is a (paracompact) csσ-space when equipped with either the compact-open or the cs-open topology. It is proved that the compact sets are the same in the two topologies. The class of cs σ-spaces and the class of -spaces introduced by 0 ‘Meara are shown to be identical in the presence of paracompactness.

Mathematical Subject Classification 2000
Primary: 54C35
Milestones
Received: 18 February 1971
Revised: 15 November 1972
Published: 1 August 1973
Authors
Joe Alston Guthrie