Preclosure operator and its applications in general topology

الموضوعات :

A. A. Nasef ¹ (Department of Physics and Engineering Mathematics, Faculty of Engineering, Kafr El-Sheikh University, Kafr El-Sheikh, Egypt)
S. Jafari ² (College of Vestsjaelland South, Herrestraede 11, 4200 Slagelse, Denmark)
M. Caldas ³ (Departamento de Mathematica Aplicada, Universidade Federal Fluminense, Rua Mario Santos Braga, s/n24020-140, Niteroi, RJ Brasil)
R. M. Latif ⁴ (Department of Mathematics and statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia)
A. A. Azzam ⁵ (Department of Mathematics, Faculty of Science, Assuit University, New Valley, Egypt)

تاريخ الإرسال : 13 الإثنين , شوال, 1437 تاريخ التأكيد : 09 الجمعة , جمادى الأولى, 1439 تاريخ الإصدار : 13 الخميس , جمادى الثانية, 1439

الکلمات المفتاحية: Preclosure-separated, preclosure functions, precontinuous functions,

ملخص المقالة :

In this paper, we show that a pointwise symmetric pre-isotonic preclosurefunction is uniquely determined the pairs of sets it separates. We then showthat when the preclosure function of the domain is pre-isotonic and the pre-closure function of the codomain is pre-isotonic and pointwise-pre-symmetric,functions which separate only those pairs of sets which are already separatedare precontinuous.

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