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Extension Closed and Cluster Closed Subspaces

Published online by Cambridge University Press:  20 November 2018

Douglas Harris
Douglas Harris*
Affiliation:
Marquette University, Milwaukee, Wisconsin
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One of the most useful properties of a compact Hausdorff space is that such a space is closed whenever embedded into a Hausdorff space. This property does not extend to compact spaces with respect to embeddings into arbitrary spaces. Thus, an interesting topological problem is to characterize the types of absolute “closure” properties that are possessed by compact spaces. This is the problem that is solved in the present paper.

The following notation and terminology will be used below. We shall consider a fixed space X and subspace A, representing arbitrary nonempty open subsets of X (respectively A ) by W (respectively V).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 24 , Issue 6 , December 1972 , pp. 1132 - 1136
Copyright
Copyright © Canadian Mathematical Society 1972

References

1. Douglas, Harris, Douglas, Harris, Structures in topology, Mem. Amer. Math. Soc, No. 115.Google Scholar
2. Douglas, Harris, Compact spaces and products of finite spaces, Proc. Amer. Math. Soc. 35 (1972), 275–280.Google Scholar
3. Douglas, Harris, Universal compact T1 spaces (to appear in General Topology and Appl.).Google Scholar