Volume 20 • Issue 2 • PP: 77-85 • 2023
A new class of NeutroOpen, NeutroClosed, AntiOpen and AntiClosed sets in NeutroTopological and AntiTopological spaces
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A lot of research has been done on the types of open and closed sets in general topological spaces and also in general bitopological spaces. Types of sets like pre-open sets and pre-closed sets, semi-open sets and semi-closed sets, Alpha-open sets, and Alpha-closed sets, regular open sets and regular closed sets, g-open sets and g-closed sets, and many more have been defined and studied. In the current study, an attempt has been made to define and give examples of a new category of open and closed sets, namely, NeutroOpen and NeutroClosed sets. Further, the concept of neutron-topology is used to define NeutroPreOpen and NeutroPreClosed sets, NeutroSemiOpen and NeutroSemiClosed sets, NeutroAlphaOpen and NeutroAlphaClosed sets, NeutroRegularOpen and NeutroRegularClosed sets, NeutroBetaOpen, and NeutroBetaClosed sets, and several examples have been given to illustrate each of the new classes of sets. Also, the concept of AntiTopology has been used to define another class of sets, namely, AntiOpen and AntiClosed sets of the above five classes of sets, namely, regular-open/closed; semi-open/closed, Alpha-open/closed, Beta-open/closed pre-open/closed sets. Further, a new class of subsets is identified which are named as NeutroTauOpen and NeutroTauClosed sets. Similar subsets in anti-topological spaces are named as AntiTauOpen and AntiTauClosed sets.
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References
[1] Andrijevic D., Semi-preopen sets, Mat. Vesink, 38(1986), 24 – 32.
[2] Basumatary B., Khaklary J.K. (2022). A Study on the Properties of AntiTopological Space. Neutrosophic Algebraic Structures and Their Applications, Chapter 2/pp: 16-27.
[3] Basumatary B., Khaklary J.K., Wary N., &Smarandache F. (2022). On some properties of
NeutroTopological Space. Theory and Applications of NeutroAlgebras as Generalizations of Classical Algebras, 180 – 201.
[4] H. Corson and E. Michael, Metrizability of certain countable unions, Illinois J. Math.8(1964), 351-360.
[5] Levine.N, Semi-open sets and semi-continuity in topological space, Amer. Math. Monthly, 70(1) (1963), 36-41.
[6] Mashhour.A.S.,Abd El-Monsef.M.E., and El-Deeb.S.N., On Precontinuous and weak precontinuous mappings. Proc. Math, Phys, Soc. Egypt, 53 (1982), 47-53.
[7] Njastad. O., On Some Classes of Nearly Open sets, Pacific J. Math. 15(1965) No. (3), 961 970.
[8] Sahin, M., Kargın, A., &Yücel, M. (2021). Neutro-Topological Space and Anti-Topological Space. NeutroAlgebra Theory, Volume I, 16-30.
[9] Stone. M, Application of the theory of Boolean rings to general topology, Trans.Amer.Math.Soc., 41(1937), 374-481.
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