An Ascoli theorem for sequential spaces
Ascoli theorems characterize precompact subsets of the set of morphisms between two objects of a category in terms of equicontinuity and pointwise precompactness, with appropriate definitions of precompactness and equicontinuity in the studied category. An Ascoli theorem is presented for sets of con...
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| Format: | Article |
| Language: | English |
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Wiley
2001-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171201004264 |
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| _version_ | 1832563530975412224 |
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| author | Gert Sonck |
| author_facet | Gert Sonck |
| author_sort | Gert Sonck |
| collection | DOAJ |
| description | Ascoli theorems characterize precompact subsets of the set of morphisms between two objects of a category in terms of equicontinuity and pointwise precompactness, with appropriate definitions of precompactness and equicontinuity in the studied category. An Ascoli theorem is presented for sets of continuous functions from a sequential space to a uniform space. In our development we make extensive use of the natural function space structure for sequential spaces induced by continuous convergence and define appropriate concepts of equicontinuity for sequential spaces. We apply our theorem in the context of C*-algebras. |
| format | Article |
| id | doaj-art-ec72c10e78904fd09ad12d085225d9be |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2001-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-ec72c10e78904fd09ad12d085225d9be2025-02-03T01:20:04ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252001-01-0126530331510.1155/S0161171201004264An Ascoli theorem for sequential spacesGert Sonck0Vrije Universiteit Brussel, Department Wiskunde, Pleinlaan 2, Brussel B-1050, BelgiumAscoli theorems characterize precompact subsets of the set of morphisms between two objects of a category in terms of equicontinuity and pointwise precompactness, with appropriate definitions of precompactness and equicontinuity in the studied category. An Ascoli theorem is presented for sets of continuous functions from a sequential space to a uniform space. In our development we make extensive use of the natural function space structure for sequential spaces induced by continuous convergence and define appropriate concepts of equicontinuity for sequential spaces. We apply our theorem in the context of C*-algebras.http://dx.doi.org/10.1155/S0161171201004264 |
| spellingShingle | Gert Sonck An Ascoli theorem for sequential spaces International Journal of Mathematics and Mathematical Sciences |
| title | An Ascoli theorem for sequential spaces |
| title_full | An Ascoli theorem for sequential spaces |
| title_fullStr | An Ascoli theorem for sequential spaces |
| title_full_unstemmed | An Ascoli theorem for sequential spaces |
| title_short | An Ascoli theorem for sequential spaces |
| title_sort | ascoli theorem for sequential spaces |
| url | http://dx.doi.org/10.1155/S0161171201004264 |
| work_keys_str_mv | AT gertsonck anascolitheoremforsequentialspaces AT gertsonck ascolitheoremforsequentialspaces |