International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 76162, 5 pages
A characterization of open mapping in terms of convergent sequences
Department of Mathematics and Statistics, Oakland University, Rochester 48309, MI, USA
Received 5 March 2005; Revised 4 January 2006; Accepted 22 January 2006
Copyright © 2006 Irwin E. Schochetman. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.