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