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Proceedings of the American Mathematical Society

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Dimension-theoretic properties of completions

Author: B. R. Wenner
Journal: Proc. Amer. Math. Soc. 28 (1971), 590-594
MSC: Primary 54.70
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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  • [1] K. Nagami, Some theorems in dimension theory for non-separable spaces, J. Math. Soc. Japan 9 (1957), 80-92. MR 18, 918. MR 0084766 (18:918c)
  • [2] J. Nagata, Modern dimension theory, Bibliotheca Math., vol. 6, Interscience, New York, 1965. MR 34 #8380.
  • [3] B. R. Wenner, Dimension on boundaries of $ \varepsilon $-spheres, Pacific J. Math. 27 (1968), 201-210. MR 38 #2735. MR 0234418 (38:2735)
  • [4] -, Remetrization in strongly countable-dimensional spaces, Canad. J. Math. 21 (1969), 748-750. MR 39 #3453. MR 0242119 (39:3453)
  • [5] -, Extending maps and dimension theory, Duke Math. J. 37 (1970), 627-631. MR 0268868 (42:3765)

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Keywords: Dimension theory, equivalent metric, completion, compactification, locally finite collection, closure-preserving collection
Article copyright: © Copyright 1971 American Mathematical Society

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