I-Connectedness
Abstract
In this paper, we introduce a weak form of connectedness with respect to an ideal. We also investigate its relation to connectedness. We examine the I-connectedness property on the new topology introduced by the ideal. In addition, it is revealed under what conditions I-connectedness and connectedness coincide and one differs from another.
Keywords
References
- R. Vaidyanathaswamy, The Localisation Theory in Set Topology, Proceedings of the Indian Academy of Sciences 20 (1945) 51–61.
- K. Kuratowski, Topology, Volume I, Academic Press, New York, 1966.
- E. Ekici, T. Noiri, Connectedness in Ideal Topological Spaces, Novi Sad Journal of Mathematics 38 (2) (2008) 65–70.
- N. Sathiyasundari, V. Renukadevi, Note on ∗-Connected Ideal Spaces, Novi Sad Journal of Mathematics 42 (1) (2012) 15–20.
- S. Modak, T. Noiri, Connectedness of Ideal Topological Spaces, Filomat 29 (4) (2015) 661–665.
- S. Kilinc, More on ∗∗-Connectedness, Matematichki Bilten 43 (2) (2019) 53–60.
- B. K. Tyagi, M. Bhardwaj, S. Singh, Cl*-Connectedness and Cl-Cl*-Connectedness in Ideal Topological Spaces, Matematichki Bilten 42 (2) (2018) 91–100.
- D. Jankovic, T. R. Hamlett, New Topologies from Old via Ideals, The American Mathematical Monthly 97(4) (1990) 295–310.
- O. Njåstad, Remarks on Topologies Defined by Local Properties, Avhandlinger Norske Videnskaps-Akademi Oslo, Universitetsforlaget, 1966.
- R. L. Newcomb, Topologies Which are Compact Modulo an Ideal, PhD Dissertation, University of California (1967) Santa Barbara, USA.