Notes on Fréchet spaces
First, we introduce sequential convergence structures and characterize Fréchet spaces and continuous functions in Fréchet spaces using these structures. Second, we give sufficient conditions for the expansion of a topological space by the sequential closure operator to be a Fréchet space and also a...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1999-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171299226592 |
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| Summary: | First, we introduce sequential convergence structures and characterize Fréchet spaces and continuous functions in Fréchet spaces using these structures. Second, we give sufficient conditions for the expansion of a topological space by the sequential closure operator to be a Fréchet space and also a sufficient condition for a simple expansion of a topological space
to be Fréchet. Finally, we study on a sufficient condition that a sequential space be Fréchet, a weakly first countable space be first countable, and a symmetrizable space be semi-metrizable. |
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| ISSN: | 0161-1712 1687-0425 |