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Some classes of E-Compactness

Published online by Cambridge University Press:  09 April 2009

Robert L. Blefko
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Mrowka and Engleking [1] have recently introduced a notion more general than that of compactness. Perhaps the most convenient direction at departure is the following: for spaces X and E, X is said to be E-compact if X is topologically embeddable as a closed subset of a product Em for some cardinal m, in which case we write X ⊂cl Em. More generally, X is said to be E-completely regular if X is topologically embeddable in a product Em for some m. For example, if we take E to be the unit interval I, we obtain the class of compact spaces and completely regular spaces, respectively, as is well-known. The question then arises, of course, given a space E, what spaces are compact with respect to it? A related question, to which we address ourselves in this note, is the following. Denote by K[E] all those topological spaces which are E-compact. Then we ask: are there very many distinct E-compact classes? It will develop that there are indeed quite a large number of such classes.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 13 , Issue 4 , June 1972 , pp. 492 - 500
Copyright
Copyright © Australian Mathematical Society 1972

References

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