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Some embeddings related to C*-embeddings

Part of: Maps and general types of spaces defined by maps Fairly general properties

Published online by Cambridge University Press:  09 April 2009

C. E. Aull
C. E. Aull
Affiliation:
Department of Mathematics Virginia Polytechnic Institute and State UniversityBlacksburg, Virginia 24061, U.S.A
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Abstract

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A space S is R*-embedded (G*-embedded) in a space X if two disjoint regular closed sets (closure disjoint open sets) of S are contained in disjoint regular closed sets (extended to closure disjoint open sets) of X. A space S is R-extendable to a space X if any regular closed set of S can be extended to a regular closed set of X. It is shown that R*-embedding and G*-embedding are identical with C*-embedding for certain fairly general classes of Tychonoff spaces. Under certain conditions it is shown that R-extendability is related to z-embedding. Spaces in which the regular open sets are C and C*-embedded are also investigated.

MSC classification

Secondary: 54C45: $C$- and $C^*$-embedding 54D15: Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 44 , Issue 1 , February 1988 , pp. 88 - 104
Copyright
Copyright © Australian Mathematical Society 1988

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