TY - JOUR
AU - Al-Omeri, Wadei
AU - Noorani, Mohd. Salmi Md.
AU - Al-Omari, A.
PY - 2014/02/04
Y2 - 2023/12/02
TI - On topological groups via a-local functions
JF - Applied General Topology
JA - Appl. Gen. Topol.
VL - 15
IS - 1
SE -
DO - 10.4995/agt.2014.2126
UR - https://polipapers.upv.es/index.php/AGT/article/view/2126
SP - 33-42
AB - An ideal on a set X is a nonempty collection of subsets<br />of X which satisfies the following conditions (1)A âˆˆ I and B âŠ‚ A implies B âˆˆ I; (2) A âˆˆ I and B âˆˆ I implies A âˆª B âˆˆ I. Given a topological space (X; ) an ideal I on X and A âŠ‚ X, â„œa(A) is defined as âˆª{U âˆˆ a : U âˆ’ A âˆˆ I}, where the family of all a-open sets of X forms a topology [5, 6], denoted by a. A topology, denoted a <br />, finer than a is generated by the basis (I; ) = {V âˆ’ I : V âˆˆ a(x); I âˆˆ I}, and a topology, denoted âŸ¨â„œa( )âŸ© coarser than a is generated by the basis â„œa( ) = {â„œa(U) : U âˆˆ a}. In this paper A bijection f : (X; ; I) â†’ (X; ;J ) is called a Aâˆ—-homeomorphism if f : (X; a ) â†’ (Y; a ) is a<br />homeomorphism, â„œa-homeomorphism if f : (X;â„œa( )) â†’ (Y;â„œa()) is a homeomorphism. Properties preserved by Aâˆ—-homeomorphism are studied as well as necessary and sufficient conditions for a â„œa-homeomorphism to be a Aâˆ—-homeomorphism.
ER -