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Proceedings of the American Mathematical Society

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

 

 

Dimension-theoretic properties of completions


Author: B. R. Wenner
Journal: Proc. Amer. Math. Soc. 28 (1971), 590-594
MSC: Primary 54.70
DOI: https://doi.org/10.1090/S0002-9939-1971-0275394-2
MathSciNet review: 0275394
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Abstract: In this paper we extend some previous work from situations involving countable collections of subsets to those concerning locally finite collections. An example of the results obtained here is a theorem which asserts that corresponding to any locally finite collection of finite-dimensional closed subsets of a metric space $ X$ there exists a completion of $ X$ in which taking the closure of any member of the given collection does not raise dimension. The basic technique employed in each of the proofs is similar; a topologically equivalent metric is introduced (one which is strongly dependent upon the given locally finite collection), and the desired completion is then taken with respect to this new metric.


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DOI: https://doi.org/10.1090/S0002-9939-1971-0275394-2
Keywords: Dimension theory, equivalent metric, completion, compactification, locally finite collection, closure-preserving collection
Article copyright: © Copyright 1971 American Mathematical Society