Vol. 108, No. 1, 1983

Recent Issues
Vol. 331: 1  2
Vol. 330: 1  2
Vol. 329: 1  2
Vol. 328: 1  2
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Vol. 324: 1  2
Online Archive
Volume:
Issue:
     
The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Officers
 
Subscriptions
 
ISSN 1945-5844 (electronic)
ISSN 0030-8730 (print)
 
Special Issues
Author index
To appear
 
Other MSP journals
On the convergence of closed and compact sets

Eva Lowen-Colebunders

Vol. 108 (1983), No. 1, 133–140
Abstract

For a topological Hausdorff space X we study the hyperspaces 𝒫(X), 2X and 𝒞(X) of all closed subsets, all non-empty closed subsets and all non-empty compact subsets endowed with the convergence of sets. In this paper we shall work with the filter description of this convergence, as defined by Choquet [2], which however is equivalent to the topological convergence of nets of sets as defined by Frolik and Mrówka. We shall study the relation between properties of X and properties of the spaces 𝒫(X), 2X and 𝒞(X) such as compactness, local compactness, regularity and the topological and pretopological character.

Mathematical Subject Classification 2000
Primary: 54A20
Secondary: 54B20
Milestones
Received: 4 October 1979
Revised: 26 July 1982
Published: 1 September 1983
Authors
Eva Lowen-Colebunders