A study of uniformities on the space of uniformly continuous mappings
New families of uniformities are introduced on UC(X,Y)UC(X,Y), the class of uniformly continuous mappings between X and Y, where (X,U)(X,{\mathcal{U}}) and (Y,V)(Y,{\mathcal{V}}) are uniform spaces. Admissibility and splittingness are introduced and investigated for such uniformities. Net theory is...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2020-12-01
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| Series: | Open Mathematics |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/math-2020-0110 |
| Summary: | New families of uniformities are introduced on UC(X,Y)UC(X,Y), the class of uniformly continuous mappings between X and Y, where (X,U)(X,{\mathcal{U}}) and (Y,V)(Y,{\mathcal{V}}) are uniform spaces. Admissibility and splittingness are introduced and investigated for such uniformities. Net theory is developed to provide characterizations of admissibility and splittingness of these spaces. It is shown that the point-entourage uniform space is splitting while the entourage-entourage uniform space is admissible. |
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| ISSN: | 2391-5455 |