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Some bitopological concepts based on the alternative effects of closure and interior operator
Faculty
Science
Year:
2004
Type of Publication:
Article
Pages:
1119-1129
Authors:
El-Tantawy, OA, Abu-Donia, HM
DOI:
10.1016/S0960-0779(03)00299-6
Journal:
CHAOS SOLITONS \& FRACTALS PERGAMON-ELSEVIER SCIENCE LTD
Volume:
19
Research Area:
Mathematics; Physics
ISSN
ISI:000185948200013
Keywords :
Some bitopological concepts based , , alternative effects
Abstract:
In this paper we give an approach for constructing classes of near open and near closed sets which have unusual implication relations. These new classes of subsets are based on the alternative effect of closure and interior operators with respect to two topologies. Also these classes of subsets are applied for constructing several classes of near continuous functions and some types of separation axioms called mildly binormal, almost ij-normal, almost ij-regular, quasi ij-regular and strongly S-ij-regular. Using the introduced functions, we generalize several preservation theorems of normality and regularity to bitopological spaces. Implications between notions are given and counter examples for some reverse directions are obtained. It should be noted that considering the space time as the product of two topologies, the topology of space and that of the space time will open the way for new line of research in the field of quantum gravity initiated by Witten and El-Naschie and many others (cf. {[}Chaos, Solitons \& Fractals 17 (2003) 989; Chaos, Solitons \& Fractals 7 (1996) 499; Int. J. Theor. Phys. 37 (1998) 2935; Phys. Today (1996) 24]). (C) 2003 Elsevier Ltd. All rights reserved.
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