Vol. 20, No. 3, 1967

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Mappings and spaces

Takesi Isiwata

Vol. 20 (1967), No. 3, 455–480

Let φ be a closed continuous mapping from X onto Y. It is an open problem whether the realcompactness of X implies the realcompactness of Y. Concerning this problem, in case φ is an open WZ-mapping, we discuss the structure of the image space Y under φ and give a necessary and sufficient condition that Y be realcompact. We also show that if X is locally compact, countably paracompact, normal space then the image space Y of X under a closed mapping is realcompact when X is realcompact.

Mathematical Subject Classification
Primary: 54.60
Received: 17 July 1964
Published: 1 March 1967
Takesi Isiwata