Vol. 84, No. 2, 1979

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Ultra-Hausdorff H-closed extensions

Jack Ray Porter and R. Grant Woods

Vol. 84 (1979), No. 2, 399–411

Introduction. A Hausdorff topological space X is called ultra-Hausdorff if, given two distinct points p and q of X, there is an open-and-closed (henceforth called “clopen”) subset A of X such that p A and qA. A Hausdorff space X is H-closed if, whenever it is embedded as a subspace of another Hausdorff space Y , it is a closed subset of Y . In this paper we characterize those Hausdorff spaces that have ultra-Hausdorff H-closed extensions and construct, for such spaces, the projective maximum of the set of ultra-Hausdorff H-closed extensions. We compare this projective maximum to the Katětov H-closed extension, and examine when continuous functions can be continuously extended to this projective maximum.

Mathematical Subject Classification 2000
Primary: 54D35
Secondary: 54D15
Received: 16 October 1978
Published: 1 October 1979
Jack Ray Porter
R. Grant Woods