International Journal of Neutrosophic Science

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https://doi.org/10.54216/IJNS

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Volume 24 , Issue 3 , PP: 77-84, 2024 | Cite this article as | XML | Html | PDF | Full Length Article

A new generalized topology coarser than the old generalized topology

Jos´e Sanabria 1 * , Alexandra Barroso 2 , Jorge Vielma 3

  • 1 Department of Mathematics, Faculty of Education and Sciences, Universidad de Sucre, Sincelejo, Colombia - (jesanabri@gmail.com)
  • 2 Department of Mathematics, Faculty of Education and Sciences, Universidad de Sucre, Sincelejo, Colombia - (alexandra.barroso@unisucre.edu.co)
  • 3 Department of Mathematics, Faculty of Natural Sciences and Mathematics, Escuela Superior Polit´ecnica del Litoral (ESPOL), Campus Gustavo Galindo, Guayaquil, Ecuador - (jevielma@espol.edu.ec)
  • Doi: https://doi.org/10.54216/IJNS.240307

    Received: October 18, 2023 Revised: February 19, 2024 Accepted: May 02, 2024
    Abstract

    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.

    Keywords :

    Generalized topology , &mu , -open , &mu , -base , &mu , -regular space

    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.

    Cite This Article As :
    Sanabria, Jos´e. , Barroso, Alexandra. , Vielma, Jorge. A new generalized topology coarser than the old generalized topology. International Journal of Neutrosophic Science, vol. , no. , 2024, pp. 77-84. DOI: https://doi.org/10.54216/IJNS.240307
    Sanabria, J. Barroso, A. Vielma, J. (2024). A new generalized topology coarser than the old generalized topology. International Journal of Neutrosophic Science, (), 77-84. DOI: https://doi.org/10.54216/IJNS.240307
    Sanabria, Jos´e. Barroso, Alexandra. Vielma, Jorge. A new generalized topology coarser than the old generalized topology. International Journal of Neutrosophic Science , no. (2024): 77-84. DOI: https://doi.org/10.54216/IJNS.240307
    Sanabria, J. , Barroso, A. , Vielma, J. (2024) . A new generalized topology coarser than the old generalized topology. International Journal of Neutrosophic Science , () , 77-84 . DOI: https://doi.org/10.54216/IJNS.240307
    Sanabria J. , Barroso A. , Vielma J. [2024]. A new generalized topology coarser than the old generalized topology. International Journal of Neutrosophic Science. (): 77-84. DOI: https://doi.org/10.54216/IJNS.240307
    Sanabria, J. Barroso, A. Vielma, J. "A new generalized topology coarser than the old generalized topology," International Journal of Neutrosophic Science, vol. , no. , pp. 77-84, 2024. DOI: https://doi.org/10.54216/IJNS.240307