Author/Authors :
Nasef, A. A. Department of Physics and Engineering Mathematics - Faculty of Engineering - Kafr El-Sheikh University, Egypt. , Jafari, S. College of Vestsjaelland South, Herrestraede, Denmark , Caldas, M. Departamento de Mathematica Aplicada - Universidade Federal Fluminense, Brasil , Latif, R. M. Department of Mathematics and statistics - King Fahd University of Petroleum and Minerals Dhahran, Saudi Arabia , Azzam, A. A. Department of Mathematics - Faculty of Science - Assuit University, New Valley, Egypt
Abstract :
In this paper, we show that a pointwise symmetric pre-isotonic preclosure function
is uniquely determined the pairs of sets it separates. We then show that when the preclosure function of the domain is pre-isotonic and the preclosure function of the codomain is pre- isotonic and pointwise-pre-symmetric, functions which separate only those pairs of sets which are already separated are precontinuous.
