Open Access
May 2009 Limit Sets and Closed Sets in Separable Metric Spaces
Candyce Hecker, Richard P. Millspaugh
Missouri J. Math. Sci. 21(2): 78-82 (May 2009). DOI: 10.35834/mjms/1316027240


Example 2 in Chapter 5 of [1] constructs, for an arbitrary closed subset of the real line, a sequence whose set of limit points is exactly the original closed set. We use a similar construction to show that an arbitrary nonempty closed set in a separable metric space is always the set of limit points of some sequence. We note further that if all nonempty closed subsets of a metric space can be realized as sets of limit points of sequences, then that metric space is separable.


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Candyce Hecker. Richard P. Millspaugh. "Limit Sets and Closed Sets in Separable Metric Spaces." Missouri J. Math. Sci. 21 (2) 78 - 82, May 2009.


Published: May 2009
First available in Project Euclid: 14 September 2011

zbMATH: 1209.54012
MathSciNet: MR2529010
Digital Object Identifier: 10.35834/mjms/1316027240

Primary: 54D65

Rights: Copyright © 2009 Central Missouri State University, Department of Mathematics and Computer Science

Vol.21 • No. 2 • May 2009
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