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...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
1999-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171299226592 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832549411336486912 |
|---|---|
| author | Woo Chorl Hong |
| author_facet | Woo Chorl Hong |
| author_sort | Woo Chorl Hong |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-ee9907f48e0e434789c7b55de3e2e7a2 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1999-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-ee9907f48e0e434789c7b55de3e2e7a22025-02-03T06:11:28ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251999-01-0122365966510.1155/S0161171299226592Notes on Fréchet spacesWoo Chorl Hong0Department of Mathematics Education, Pusan National University, Pusan 609-735, KoreaFirst, 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.http://dx.doi.org/10.1155/S0161171299226592Fréchetsequentialsequential convergence structuressequential closure operatorssimple expansionssemi-metrizablesymmetrizableweakly first countable. |
| spellingShingle | Woo Chorl Hong Notes on Fréchet spaces International Journal of Mathematics and Mathematical Sciences Fréchet sequential sequential convergence structures sequential closure operators simple expansions semi-metrizable symmetrizable weakly first countable. |
| title | Notes on Fréchet spaces |
| title_full | Notes on Fréchet spaces |
| title_fullStr | Notes on Fréchet spaces |
| title_full_unstemmed | Notes on Fréchet spaces |
| title_short | Notes on Fréchet spaces |
| title_sort | notes on frechet spaces |
| topic | Fréchet sequential sequential convergence structures sequential closure operators simple expansions semi-metrizable symmetrizable weakly first countable. |
| url | http://dx.doi.org/10.1155/S0161171299226592 |
| work_keys_str_mv | AT woochorlhong notesonfrechetspaces |