Volume 24 • Issue 3 • PP: 77-84 • 2024
A new generalized topology coarser than the old generalized topology
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In this research work, basic concepts and properties are considered within the context of a generalized topological space (X, μ), as tools to generate a new generalized topology bμ by means of a μ-base formed by the μ-interiors of μ-closed sets. This leads to an exploration of the relationship between some of the properties of the generalized topologies μ and bμ, such as generalized separation axioms, generalized connectedness, generalized continuity, generalized topological sum, and generalized product topology.
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References
[1] C. Carpintero, E. Rosas, M. Salas, J. Sanabria, μ-Compactness with respect to a hereditary class, Boletim da Sociedade Paranaense de Matem´atica 34(2) (2016), 231-236.
[2] C. Carpintero, E. Rosas, M. Salas-Brown, J. Sanabria, Minimal open sets on generalized topological spaces, Proyecciones 36(4) (2017), 739-751.
[3] A´ . Csa´sza´r, Generalized topology, generalized continuity, Acta Mathematica Hungarica 96 (2002), 351- 357.
[4] A´ . Csa´sza´r, γ-connected sets, Acta Mathematica Hungarica 101 (2003), 273-279.
[5] A´ . Csa´sza´r, Extremally disconnected generalized topologies, Annales Universitatis Scientiarum Budapestinensis de Rolando E¨otv¨os Nominatae, Sectio Mathematica 47 (2004), 91-96.
[6] A´ . Csa´sza´r, Separation axioms for generalized topologies, Acta Mathematica Hungarica 104 (2004), 63-69.
[7] A´ . Csa´sza´r, Generalized open sets in generalized topologies, Acta Mathematica Hungarica 106 (2005), 53-66.
[8] A´ . Csa´sza´r, Modification of generalized topologies via hereditary classes, Acta Mathematica Hungarica 115 (2007), 29-36.
[9] A´ . Csa´sza´r, Normal generalized topologies, Acta Mathematica Hungarica 115 (2007), 309-313.
[10] E. Ekici, Generalized hyperconnectedness, Acta Mathematica Hungarica 133 (2011), 140-147.
[11] R. Khayyeri, On base for generalized topological spaces, International Journal of Contemporary Mathematical Sciences 6 (2011), 2377-2383.
[12] E. Korczak-Kubiak, A. Loranty, R.J. Pawlak, Baire generalized topological spaces, generalized metric spaces and infinite games, Acta Mathematica Hungarica 140(3) (2013), 203-231.
[13] Z. Li, F. Lin, Baireness on generalized topological spaces, Acta Mathematica Hungarica 139 (2013), 320-336.
[14] B. Roy, On a type of generalized open sets, Applied General Topology 12(2) (2011), 163-173.
[15] B. Roy, A note on weakly (μ, λ)-closed functions, Mathematica Bohemica 138(4) (2013), 397-405.
[16] J. Sanabria, L. Maza, E. Rosas, C. Carpintero, Unified theory of the kernel of a set via hereditary classes and generalized topologies, Missouri Journal of Mathematical Sciences 35(1) (2023), 60-74.
[17] M.S. Sarsak, On μ-compact sets in μ-spaces, Questions and Answers in General Topology 31(1) (2013), 49-57.
[18] M.S. Sarsak, More on μ-semi-Lindel¨of sets in μ-spaces, Demonstratio Mathematica 54 (2021), 259-271.
[19] M.S. Sarsak, On μ-β-Lindel¨of sets in generalized topological spaces, Heliyon 9(3) (2023), e13597.
[20] R. Shen, A note on generalized connectedness, Acta Mathematica Hungarica 122 (2009), 231-235.
[21] X.Wu, P. Zhu, Generalized product topology, Communications of the Korean Mathematical Society 28(4) (2013), 819-825.
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