Vol. 68, No. 1, 1977

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On closedness of C- and Cāˆ—-embeddings

Yoshio Tanaka

Vol. 68 (1977), No. 1, 283ā€“292
Abstract

In view of weak topology, this paper studies the conditions for C-and C-embedded subsets of k-spaces to be closed. For example, we have the following: A C-embedded subset S is closed in a space X, if S is paracompact and X is a k-space. A C-embedded subset S is closed in a space X, if (1) X is a k-space in which every point is a Gδ-set; (2) S is normal, or an Fσ-set of X, and X is a sequential space; or (3) S is subparacompact, or an Fσ-set of X, and X is a k-space which is hereditarily normal, or hereditarily countably paracompact.

Mathematical Subject Classification 2000
Primary: 54D50
Milestones
Received: 2 April 1976
Revised: 15 June 1976
Published: 1 January 1977
Authors
Yoshio Tanaka