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Zero-Dimensional Compactifications of Locally Compact Spaces

Published online by Cambridge University Press:  20 November 2018

R. Grant Woods
R. Grant Woods*
Affiliation:
University of Manitoba, Winnipeg, Manitoba
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Let X be a locally compact Hausdorff topological space. A compactification of X is a compact Hausdorff space which contains X as a dense subspace. Two compactifications αX and γX of X are equivalent if there is a homeomorphism from αX onto γX that fixes X pointwise. We shall identify equivalent compactifications of a given space. If is a family of compactifications of X, we can partially order by saying that αX ≦ γX if there is a continuous map from γX onto αX that fixes X pointwise.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 4 , August 1974 , pp. 920 - 930
Copyright
Copyright © Canadian Mathematical Society 1974

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