α-local function and its properties in ideal topological spaces

• Autorzy: Al-Omeri W. F. , Noorani M.S.M. , Al-Omar A.
• Języki publikacji: EN

Abstrakty

EN

In this paper, we introduce the notation of a-local function and study its properties in ideal topological space. We construct a topology т^a* for X by using a-open set and an Ʈ on X. We defined a-compatible of т with ideal and show that т is a-compatible with Ʈ then т^a* - β(Ʈ, т), where β(Ʈ, т) - {V-I : V € т^a (x), I € Ʈ} is a basis of т^a* Also, The relationships other local functions such as local function [12, 6] and semi-local function [7] are introduced.

Słowa kluczowe

EN

ideal topological space; a-local function; a-open set

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2014
• Tom: Nr 53
• Strony: 5--15
• Opis fizyczny: Bibliogr. 13 poz.

Twórcy

autor

Al-Omeri W. F.

• School of Mathematical Sciences Faculty of Science and Technology Universiti Kebangsaan Malaysia 43600 UKM Bangi, Selangor DE, Malaysia

autor

Noorani M.S.M.

• School of Mathematical Sciences Faculty of Science and Technology Universiti Kebangsaan Malaysia 43600 UKM Bangi, Selangor DE, Malaysia

autor

Al-Omar A.

• Ahmad Al-omari Department of Mathematics Faculty of Science Al AL-Bayat University P.O.Box 130095, Mafraq 25113, Jordan

Bibliografia

• [1] Crossley S.G., Hildebrand S.K., Semi-closure, Texas J. Sci, 22(1971), 99-112.
• [2] Ekici E., A note on a-open sets and e*-open sets, Filomat, 22(1)(2008), 89-96.
• [3] Ekici E., On a-open sets, A*-sets and decompositions of continuity and super-continuity, Annales Univ. Sci. Budapest., 51(2008), 39-51.
• [4] Hamlett T.R., Rose D., Remarks on some theorems of banach, mcshans, and pettis, Rocky Mountain J. of Math., 22(4)(1992), 1329-1339.
• [5] Hayashi E., Topologies defined by local properites, Math. Ann., 156(1964), 205-215.
• [6] Jankovic D., Hamlett T.R., New topologies from old via ideals, Amer. Math. Monthly, 97(1990), 295-310.
• [7] Khan M., Noiri T., Semi-local functions in ideal topological spaces, J. Adv. Res. Pure Math., 2(1) 2010, 36-42.
• [8] Kuratowski K., Topology, Vol. I. New York: Academic Press, 1966.
• [9] Levine N., Semi-open oets and semi-continuity in topological spaces, Amer. Math. Monthly, 70(1963), 36-41.
• [10] Stone M.H., Application of the theory of boolean rings to general topology, Trans. Amer. Math. Soc., 41(1937), 375-481.
• [11] Velicko N.V., H-closed topological spaces, Amer. Math. Soc. Trans., 78(2)(1968), 103-118.
• [12] Vaidyanathaswamy R., The localization theory in set-topology, Proc. Indian Acad. Sci., 20(1945), 51-61.
• [13] Vaidyanathaswamy R., Set topology, Chelsea Publishing Company, 1960.