TY - JOUR
AU - Bouziad, Ahmed
PY - 2019/10/01
Y2 - 2023/03/22
TI - On proximal fineness of topological groups in their right uniformity
JF - Applied General Topology
JA - Appl. Gen. Topol.
VL - 20
IS - 2
SE -
DO - 10.4995/agt.2019.11605
UR - https://polipapers.upv.es/index.php/AGT/article/view/11605
SP - 419-430
AB - <p>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 âˆˆ G : g(A) âŠ‚ B}, A, B âŠ‚ N.</p>
ER -