Vol. 55, No. 2, 1974

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On completeness and semicompleteness of first countable spaces

Joylyn Newberry Reed

Vol. 55 (1974), No. 2, 553–563

In this paper, well known completeness conditions in Moore spaces are generalized to arbitrary first countable spaces. Relationships are established between these conditions and various other completeness concepts including Čech completeness, countable completeness, and countable subcompactness. Finally, conditions are given for embedding a given first countable space in a “first countable complete” space. As one application of the theory developed, a necessary and sufficient condition is obtained for the embedding of a Moore space in a semicomplete or “Rudin” complete Moore space.

Mathematical Subject Classification 2000
Primary: 54E30
Received: 30 March 1973
Published: 1 December 1974
Joylyn Newberry Reed