A characterization of open mapping in terms of convergent sequences

Irwin E. Schochetman

International Journal of Mathematics and Mathematical Sciences, 2006, vol. 2006, 1-5

Abstract:

It is certainly well known that a mapping between metric spaces iscontinuous if and only if it preserves convergent sequences. Doesthere exist a comparable characterization for the mapping to beopen? Of course, the inverse mapping is set-valued, in general. Inthis research/expository note, we show that a mapping is open ifand only if the set-valued inverse mapping preserves convergentsequences in an appropriate set-theoretic sense.

Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:076162

DOI: 10.1155/IJMMS/2006/76162

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