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...
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Universitat Politècnica de València
2019-10-01
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| Series: | Applied General Topology |
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| Online Access: | https://polipapers.upv.es/index.php/AGT/article/view/11605 |
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doaj-d5387e7760d446918d5b7bfd2ff093df2020-11-25T00:08:53ZengUniversitat Politècnica de ValènciaApplied General Topology1576-94021989-41472019-10-0120241943010.4995/agt.2019.116057661On proximal fineness of topological groups in their right uniformityAhmed Bouziad0Université de RouenA 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.https://polipapers.upv.es/index.php/AGT/article/view/11605uniform spacetopological groupproximal continuityproximally fine groupsymmetric groupo-radial space |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Ahmed Bouziad |
| spellingShingle |
Ahmed Bouziad On proximal fineness of topological groups in their right uniformity Applied General Topology uniform space topological group proximal continuity proximally fine group symmetric group o-radial space |
| author_facet |
Ahmed Bouziad |
| author_sort |
Ahmed Bouziad |
| title |
On proximal fineness of topological groups in their right uniformity |
| title_short |
On proximal fineness of topological groups in their right uniformity |
| title_full |
On proximal fineness of topological groups in their right uniformity |
| title_fullStr |
On proximal fineness of topological groups in their right uniformity |
| title_full_unstemmed |
On proximal fineness of topological groups in their right uniformity |
| title_sort |
on proximal fineness of topological groups in their right uniformity |
| publisher |
Universitat Politècnica de València |
| series |
Applied General Topology |
| issn |
1576-9402 1989-4147 |
| publishDate |
2019-10-01 |
| description |
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. |
| topic |
uniform space topological group proximal continuity proximally fine group symmetric group o-radial space |
| url |
https://polipapers.upv.es/index.php/AGT/article/view/11605 |
| work_keys_str_mv |
AT ahmedbouziad onproximalfinenessoftopologicalgroupsintheirrightuniformity |
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1725414005805154304 |