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# Separating H-sets by Open Sets

Published:2010-04-06
Printed: Jun 2010
• Jack Porter,
Department of Mathematics, University of Kansas, Lawrence, KS 66045, USA
• Mohan Tikoo,
Department of Mathematics, Southeast Missouri State University, Cape Girardeau, MO 63701, USA
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## Abstract

In an H-closed, Urysohn space, disjoint H-sets can be separated by disjoint open sets. This is not true for an arbitrary H-closed space even if one of the H-sets is a point. In this paper, we provide a systematic study of those spaces in which disjoint H-sets can be separated by disjoint open sets.
 Keywords: H-set, H-closed, θ, -continuous
 MSC Classifications: 54C08 - Weak and generalized continuity 54D10 - Lower separation axioms ($T_0$--$T_3$, etc.) 54D15 - Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.)