The Some Properties of Beta Hat Generalized Closed Set in Generalized Topological Spaces
- closed set,
- generalized topological spaces,
- beta hat generalized closed set,
Copyright (c) 2019 International Journal For Research In Mathematics And Statistics (ISSN: 2208-2662)
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
This study introduced the concept of beta hat generalized closed set in generalized topological spaces. It also investigated related concepts such as - -interior and - -closure of a set. This paper proved that every -open (resp. -closed) set is - -open (resp. - -closed). It is also shown that the family of all - -open subsets in X does not always form a generalized topology in X. Moreover, - -closure of set is smaller than -closure while the - -interior is generally larger than its -interior.
- N. Levine, Generalized Closed Sets in Topology, Rend. Circ. Mat. Palermo, 19 (2) (1970), 89-96.
- K. Kannan and N. Nagaveni, On -Generalized Closed Sets and Open Sets in Topological Spaces, International Journal of Mathematical Analysis, Vol. 6, 2012, no.57, 2819-2828.
- Császár, Á., Generalized Topology, Generalized Continuity, Acta Mathematica Hungaria 96 (2002), 351-357.
- Dugundji, J., Topology, New Delhi Prentice Hall of India Private Ltd., 1975.
- M.Stone, Application of the theory of Boolean rings to general topology, Trans. Amer. Math. Soc., 41(1937), 374 – 481.
- Császár, Á., Generalized Open Sets in Generalized Topologies, Acta Mathematica Hungaria 106 (2005), 53-56.
- Orge, K., Some Forms of Generalized Closed Sets in Generalized Topologies, Thesis, Mindanao State University-Iligan Institute of Technology, March 2012.
- N. Levine, Generalized Closed Sets in Topology, Rend. Circ. Mat. Palermo, 19 (2) (1970), 82-88.
- Lipschutz, S., Ph. D., Schaum’s Outline of Theory and Problems of General Topology, McGraw-Hill Incorporated, United States, 1965.
- Tampos, M.L., Alpha Generalized Closed Sets in Generalized and Bigeneralized Topological Spaces, Thesis, Bohol Island State University – Main Campus, March 2016
- Baculta, J. J. Regular Generalized Star b-sets in Generalized, Bigeneralized and Generalized Fuzzy Topological Spaces, Dissertation. Mindanao State University – Iligan Insitutute of Technology, May 2015.
- Császár, Á., Generalized Open Sets in Generalized Topologies, Acta Mathematica Hungaria 106 (1-2) (2002), 351-357.
- Levine, N., Generalized Closed Sets in Topology, Rend. Circ. Mat. Palermo, 19 (1982), 82-88, 89-96.
- Császár, Á., Generalized Open Sets in Generalized Topologies, Acta Mathematica Hungaria 120 (2008), 275-279.
- Njastad, O., On Some Classes of Nearly Open Sets, Pacific Journal Math, 15 (1965), 961-970.
- Barbe M. R. Stadler and Peter F. Stadler, Generalized Topological Spaces in Evolutionary Theory and Combinatorial Chemistry. (2001)
- Wright, S., The Roles of Mutation, Inbreeding, Crossbreeding and Selection in Evolution. In: Jones, D. F., ed., Int. Proceedings of the Sixth International Congress on Genetics. Vol.1, (1932) 356-366.
- Palaniappan N and Rao KC (1993) Regular generalized closed sets, Kyunpook Math. J33: 211-219.
- Benchalli S.S., Wali R.S., On rw-Closed Sets in Topological Spaces. Bulliten of the Malaysian Mathematical Sciences Society. (2)30(2)(2007), 99-110.
- Duangphui, T., Boonpok, C., Viriyapong C., Continuous Functions on Bigeneralized Topological Spaces. Int. Journal of Math. Analysis Vol.5,2011, no.24, 1165-1174.