Preclosure operator and its applications in general topology

Subject Areas : History and biography

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)

Received: 2016-07-18 Accepted : 2018-01-26 Published : 2018-03-01

Keywords: Preclosure-separated, preclosure functions, precontinuous functions,

Abstract :

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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