@article{Al-Omeri_Noorani_Al-Omari_2014, title={On topological groups via a-local functions}, volume={15}, url={https://polipapers.upv.es/index.php/AGT/article/view/2126}, DOI={10.4995/agt.2014.2126}, abstractNote={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.}, number={1}, journal={Applied General Topology}, author={Al-Omeri, Wadei and Noorani, Mohd. Salmi Md. and Al-Omari, A.}, year={2014}, month={Feb.}, pages={33–42} }