International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Issue 2, Article ID 76162, 5 pages
doi:10.1155/IJMMS/2006/76162

A characterization of open mapping in terms of convergent sequences

Abstract

It is certainly well known that a mapping between metric spaces is continuous if and only if it preserves convergent sequences. Does there exist a comparable characterization for the mapping to be open? Of course, the inverse mapping is set-valued, in general. In this research/expository note, we show that a mapping is open if and only if the set-valued inverse mapping preserves convergent sequences in an appropriate set-theoretic sense.