On proximal fineness of topological groups in their right uniformity
A uniform space X is said to be proximally fine if every proximally continuous function defined on X into an arbitrary uniform pace Y is uniformly continuous. We supply a proof that every topological group which is functionally generated by its precompact subsets is proximally fine with respect to i...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Universitat Politècnica de València
2019-10-01
|
| Series: | Applied General Topology |
| Subjects: | |
| Online Access: | https://polipapers.upv.es/index.php/AGT/article/view/11605 |
| Summary: | A uniform space X is said to be proximally fine if every proximally continuous function defined on X into an arbitrary uniform pace Y is uniformly continuous. We supply a proof that every topological group which is functionally generated by its precompact subsets is proximally fine with respect to its right uniformity. On the other hand, we show that there are various permutation groups G on the integers N that are not proximally fine with respect to the topology generated by the sets {g ∈ G : g(A) ⊂ B}, A, B ⊂ N. |
|---|---|
| ISSN: | 1576-9402 1989-4147 |