On Submaximality in Intuitionistic Topological Spaces
In this study, a minimal submaximal element of LIT(X) (the lattice of all intuitionistic topologies for X, ordered by inclusion) is determined. Afterwards, a new contractive property, intuitionistic mega-connectedness, is defined. We show that the submaximality and mega-connectedness are not complementary intuitionistic topological invariants by identifying those members of LIT(X) which are intuitionistic mega-connected.
[1] K. Atanassov, Intuitionistic Fuzzy Sets, VII ITKR's Session, Sofia (September, 1983) (In Bulgarian). [2] N.Bourbaki, Elements De Mathematique, Topologie Generale (3rd Ed.). (Actualities Scientifques Et Industrielles 1142, Hermann, Paris, 1961). [3] J. Cao, M. Ganster And I. Reilly, Submaximality, Extremal Disconnectedness And Generalized Closed Sets, Houston Journal Of Mathematics 24 (4) (1998) 681-688 [4] D.E.Cemaron, A Survey Of Maximal Topological Spaces, Topology Proc., 2 (1997), 11-60 [5] D. Çoker, A Note On Intuitionistic Sets And Intuitonistic Points, Turkish J.Math. 20.3 (1996), 343-351 [6] D. Çoker, An Introduction To Fuzzy Intuitionistic Topological Spaces, Fuzzy Sets And Systems 88-1 (1997) 81-89 [7] D. Çoker, An Introduction To Intuitionistic Topological Spaces, BUSEFAL 81 (2000), 51-56. [8] J.Dontchev, On Submaximality Spaces, Tamhang J.Math.(3), 26 (1995), 243-250 [9] J. Dontchev, D. Rose, An Ideal Approach Submaximality, Topology Atlas (1996) [10] T. Dube, Submaximality In Locales, Topology Proceedings 29 (2) , (2005) 431-444 [11] E. Hewitt, A Problem Of Set Theoretic Topology, Duke Math. J.,10 (1943), 309-393 [12] G.J. Kennedy And S.D. Mc Cartan, Submaximality And Supraconnectedness Are Complementary Topological Invariants, Procedings Of The 8th Proque Topological Symposium (1996) [13] R.E Larson, Complementary Topological Properties, Notice Amer.Math. Soc., 20 (1973), 176 [14] S.D. Mccartan And A.E. Mc Cluskey, T0 And Loosely Nested Are Not Complementary, Proceedings Of The Eighth Prague Topological Symposium August 18-24, 1996, Prague, Czech Republic [15] A.Z.Ozcelik, S.Narli, Intuitionistic Submaximal Space, XI. Math. Symposium (1999) Turkey,182-187 [16] A.Varhangel'skit And P.J.Colins, On Submaximal Space, Topology Appl., 64 (1995), 219-241. [17] E.K Van Douwen, Applications of Maximal Topologies, Topology and Applications 51 (1993) 125-139 North-Holland.
[1] K. Atanassov, Intuitionistic Fuzzy Sets, VII ITKR's Session, Sofia (September, 1983) (In Bulgarian). [2] N.Bourbaki, Elements De Mathematique, Topologie Generale (3rd Ed.). (Actualities Scientifques Et Industrielles 1142, Hermann, Paris, 1961). [3] J. Cao, M. Ganster And I. Reilly, Submaximality, Extremal Disconnectedness And Generalized Closed Sets, Houston Journal Of Mathematics 24 (4) (1998) 681-688 [4] D.E.Cemaron, A Survey Of Maximal Topological Spaces, Topology Proc., 2 (1997), 11-60 [5] D. Çoker, A Note On Intuitionistic Sets And Intuitonistic Points, Turkish J.Math. 20.3 (1996), 343-351 [6] D. Çoker, An Introduction To Fuzzy Intuitionistic Topological Spaces, Fuzzy Sets And Systems 88-1 (1997) 81-89 [7] D. Çoker, An Introduction To Intuitionistic Topological Spaces, BUSEFAL 81 (2000), 51-56. [8] J.Dontchev, On Submaximality Spaces, Tamhang J.Math.(3), 26 (1995), 243-250 [9] J. Dontchev, D. Rose, An Ideal Approach Submaximality, Topology Atlas (1996) [10] T. Dube, Submaximality In Locales, Topology Proceedings 29 (2) , (2005) 431-444 [11] E. Hewitt, A Problem Of Set Theoretic Topology, Duke Math. J.,10 (1943), 309-393 [12] G.J. Kennedy And S.D. Mc Cartan, Submaximality And Supraconnectedness Are Complementary Topological Invariants, Procedings Of The 8th Proque Topological Symposium (1996) [13] R.E Larson, Complementary Topological Properties, Notice Amer.Math. Soc., 20 (1973), 176 [14] S.D. Mccartan And A.E. Mc Cluskey, T0 And Loosely Nested Are Not Complementary, Proceedings Of The Eighth Prague Topological Symposium August 18-24, 1996, Prague, Czech Republic [15] A.Z.Ozcelik, S.Narli, Intuitionistic Submaximal Space, XI. Math. Symposium (1999) Turkey,182-187 [16] A.Varhangel'skit And P.J.Colins, On Submaximal Space, Topology Appl., 64 (1995), 219-241. [17] E.K Van Douwen, Applications of Maximal Topologies, Topology and Applications 51 (1993) 125-139 North-Holland.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:53117", author = "Ahmet Z. Ozcelik and Serkan Narli", title = "On Submaximality in Intuitionistic Topological Spaces ", abstract = "In this study, a minimal submaximal element of LIT(X) (the lattice of all intuitionistic topologies for X, ordered by inclusion) is determined. Afterwards, a new contractive property, intuitionistic mega-connectedness, is defined. We show that the submaximality and mega-connectedness are not complementary intuitionistic topological invariants by identifying those members of LIT(X) which are intuitionistic mega-connected. ", keywords = "Intuitionistic set; intuitionistic topology;intuitionistic submaximality and mega-connectedness.", volume = "1", number = "1", pages = "42-3", }
