A characterization of open mapping in terms of convergent sequences
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 sh...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2006-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS/2006/76162 |
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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |