A characterization of open mapping in terms of convergent sequences
| Autor: | Irwin E. Schochetman |
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| Jazyk: | angličtina |
| Rok vydání: | 2006 |
| Předmět: | |
| Zdroj: | International Journal of Mathematics and Mathematical Sciences, Vol 2006 (2006) |
| Druh dokumentu: | article |
| ISSN: | 0161-1712 1687-0425 |
| DOI: | 10.1155/IJMMS/2006/76162 |
| Popis: | 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. |
| Databáze: | Directory of Open Access Journals |
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