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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 H-set, H-closed, θ, -continuous
MSC Classifications: 54C08, 54D10, 54D15 show english descriptions Weak and generalized continuity
Lower separation axioms ($T_0$--$T_3$, etc.)
Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.)
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.)
 

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