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Uniform spaces based on a way below relation

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Abstract

This paper fosters both uniform spaces and way below relations with an innovative analysis of their mutual relationships. A new concept of uniform spaces based on a way below relation (LB-fuzzifying uniform space, or LBFU space, for short) will be introduced and investigated. With this aim, first some fundamental concepts in L-fuzzifying topological spaces will be studied. Then, we shall explore some L-fuzzifying topological spaces induced by an LBFU space. Furthermore, new concepts of interior, closure, bases and subbases relative to an LBFU topology will be established. Finally, the continuity of functions between LBFU spaces will be introduced and investigated.

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Acknowledgements

The research of O. R. Sayed and O. G. Hammad was produced with the financial support of the Academy of Scientific Research and Technology (ASRT) of Egypt; ScienceUP/ GradeUp initiative: Grant Agreement No (6468). Its contents are the sole responsibility of the authors and do not necessarily reflect the views of the Academy of Scientific Research and Technology. J.C.R. Alcantud is grateful to the Junta de Castilla y León and the European Regional Development Fund (Grant CLU-2019-03) for the financial support to the Research Unit of Excellence “Economic Management for Sustainability” (GECOS).

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Assiut University, Assiut, 71516, Egypt

    O. R. Sayed & O. G. Hammad

  2. BORDA Research Unit and Multidisciplinary Institute of Enterprise (IME), University of Salamanca, Salamanca, 37008, Spain

    J. C. R. Alcantud

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  1. O. R. Sayed
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  2. O. G. Hammad
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  3. J. C. R. Alcantud
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Correspondence to O. R. Sayed.

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Sayed, O.R., Hammad, O.G. & Alcantud, J.C.R. Uniform spaces based on a way below relation. Comp. Appl. Math. 42, 2 (2023). https://doi.org/10.1007/s40314-022-02117-5

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  • DOI: https://doi.org/10.1007/s40314-022-02117-5

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