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p -Topologicalness—A Relative Topologicalness in ⊤-Convergence Spaces

Author

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  • Lingqiang Li

    (Department of Mathematics, Liaocheng University, Liaocheng 252059, China)

Abstract

In this paper, p -topologicalness (a relative topologicalness) in ⊤-convergence spaces are studied through two equivalent approaches. One approach generalizes the Fischer’s diagonal condition, the other approach extends the Gähler’s neighborhood condition. Then the relationships between p -topologicalness in ⊤-convergence spaces and p -topologicalness in stratified L -generalized convergence spaces are established. Furthermore, the lower and upper p -topological modifications in ⊤-convergence spaces are also defined and discussed. In particular, it is proved that the lower (resp., upper) p -topological modification behaves reasonably well relative to final (resp., initial) structures.

Suggested Citation

  • Lingqiang Li, 2019. "p -Topologicalness—A Relative Topologicalness in ⊤-Convergence Spaces," Mathematics, MDPI, vol. 7(3), pages 1-18, March.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:3:p:228-:d:210118
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    References listed on IDEAS

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    1. Scott A. Wilde & D. C. Kent, 1999. "p -topological and p -regular: dual notions in convergence theory," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 22, pages 1-12, January.
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    Cited by:

    1. Songtao Shao & Xiaohong Zhang, 2019. "Measures of Probabilistic Neutrosophic Hesitant Fuzzy Sets and the Application in Reducing Unnecessary Evaluation Processes," Mathematics, MDPI, vol. 7(7), pages 1-23, July.
    2. Qiu Jin & Lingqiang Li & Guangming Lang, 2019. "p -Regularity and p -Regular Modification in ⊤-Convergence Spaces," Mathematics, MDPI, vol. 7(4), pages 1-14, April.

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    1. Qiu Jin & Lingqiang Li & Guangming Lang, 2019. "p -Regularity and p -Regular Modification in ⊤-Convergence Spaces," Mathematics, MDPI, vol. 7(4), pages 1-14, April.

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