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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Proper mappings and the minimum dimension of a compactification of a space


Author: James Keesling
Journal: Proc. Amer. Math. Soc. 30 (1971), 593-598
MSC: Primary 54.70
DOI: https://doi.org/10.1090/S0002-9939-1971-0288740-0
MathSciNet review: 0288740
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Abstract: In this paper it is shown that for each positive integer n there is a locally compact Hausdorff space X having the property that $ \dim \,X = n$ and in addition having the property that if $ f(X) = Y$ is a proper mapping, then $ \dim \,Y \geqq n$. Using this result it is shown that there is a space Y having the property that $ \min \, \dim \,Y = n$ with a point $ p \in Y$ with $ \min \, \dim \, Y - \{ p\} = 0$.


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DOI: https://doi.org/10.1090/S0002-9939-1971-0288740-0
Keywords: Dimension, proper mapping, locally compact space, compactification
Article copyright: © Copyright 1971 American Mathematical Society