Vol. 106, No. 2, 1983

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Non-Hausdorff convergence spaces

R. J. Gazik

Vol. 106 (1983), No. 2, 257–264
Abstract

In this paper we will establish a method of removing the Hausdorff assumption from certain convergence space theorems. As specific applications the precise form of the closure of a compact set in a regular non-Hausdorff space is given and the exact relationship between cl and cl2 in a non-Hausdorff compact regular space is obtained. Necessary and sufficient conditions that the transition space for this procedure be topological or pretopological are found and a few embedding theorems are obtained.

Mathematical Subject Classification 2000
Primary: 54A20
Milestones
Received: 1 July 1981
Revised: 2 October 1981
Published: 1 June 1983
Authors
R. J. Gazik