Vol. 27, No. 3, 1968

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Minimal Urysohn spaces

Charles Thomas Scarborough

Vol. 27 (1968), No. 3, 611–617
Abstract

A topological space X is (1) H(i), (2) H(ii), (3) R(i), (4) R(ii) if (1) Every open filter on X has nonvoid adherence, (2) Every open filter on X with one-point adherence is convergent, (3) Every regular filter on X has nonvoid adherence, (4) Every regular filter on X with one point adherence is convergent. These properties, which were investigated by Scarborough and Stone in a recent paper, arose naturally from the study of minimal Hausdorff, H-closed, minimal regular and R-closed spaces. This paper investigates similar properties for minimal Urysohn and Urysohn closed spaces.

Mathematical Subject Classification
Primary: 54.20
Milestones
Received: 30 June 1967
Published: 1 December 1968
Authors
Charles Thomas Scarborough