Preclosure operator and its applications in general topology
محورهای موضوعی : History and biographyA. 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
کلید واژه: Preclosure-separated, preclosure functions, precontinuous functions,
چکیده مقاله :
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.
[1] M. Caldas, S. Jafari, R. M. Latif, A. A. Nasef, Semi-continuity and semi-connectedness in generalized semiclosure spaces, King Fahd University of Petroleum and Minerals, Dep. of Math. Sci. (386) (2008), 1-13.
[2] H. Corson, E. Michael, Metrizability of cerain countable uxions, Illinois J. Math. 8 (1964), 351-360.
[3] S. N. El-Deeb, I. A. Hasanein, A. S. Mashhour, T. Noiri, On p-regular spaces, Bull Math. Soc. Sci. R. S. Roumaine. 27 (57) (1983), 311-315.
[4] M. S. El-Naschie, On the uncertainty of Cantorian geometry and two slit experiment, Chaos. Solitons and Fractals. 9 (3) (1998), 517-529.
[5] E. D. Kalimsky, R. Kopperman, P. R. Meyer, Computer graphics and connected topologies on finite ordered sets, Topol. Appl. 36 (1990), 1-17.
[6] A. Kar, P. Bhattacharyya, Some weak Separation axioms, Bull. Calcutta Math. Soc. 82 (1990), 415-422.
[7] A. S. Mashhour, M. E. Abd El-Monsef, S. N. El-Deeb, On precontinuous and weak precontinuous mappings, Proc. Math. Phys. Soc. Egypt. 53 (1982), 47-53.
[8] V. Ptak, Completeness and the open mapping theorem, Bull. Soc. Math. France. 86 (1958), 41-74.
[9] M. B. Smyth, Semi-Matrices, Closure Spaces and digital topology, Theore. Comput. Sci. (5) (1995), 257-276.
