J Austral Math Soc Ser A 44 pp88--104, 1988.

Some Embeddings Related to C*-Embeddings

C. E. Aull

Abstract

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 invesigated.

1980 AMS Subject Classification: primary 54C45; secondary 54D15

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Authors

C. E. Aull

Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061, U.S.A.