Pure and Applied Mathematics Journal

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On Fuzzy Baire-Separated Spaces and Related Concepts

Received: 22 January 2024    Accepted: 27 February 2024    Published: 20 March 2024
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Abstract

In this paper, a new class of fuzzy topological spaces, namely fuzzy Baire-separated spaces is introduced in terms of fuzzy Baire sets. Several characterizations of fuzzy Baire-separated spaces are established. It is shown that fuzzy Baire sets lie between disjoint fuzzy P-sets and fuzzy Fσ- sets in a fuzzy Baire-separated space. Conditions under which fuzzy topological spaces become fuzzy Baire-separated spaces are established. Fuzzy nowhere dense sets are fuzzy closed sets in fuzzy nodec spaces and subsequently a question will arise. Which fuzzy topological spaces [other than fuzzy hyperconnected spaces, fuzzy globally disconnected spaces] have fuzzy closed sets with fuzzy nowhere denseness? For this, fuzzy topological spaces having fuzzy closed sets with fuzzy nowhere denseness are identified in this paper. It is verified that fuzzy ultraconnected spaces are non fuzzy Baire -separated spaces. The means, by which fuzzy weakly Baire space become fuzzy Baire -separated spaces and in turn fuzzy Baire - separated spaces become fuzzy seminormal spaces, are obtained. There are scope in this paper for exploring the inter-relations between fuzzy Baire spaces and Baire -separated spaces.

DOI 10.11648/j.pamj.20241301.11
Published in Pure and Applied Mathematics Journal (Volume 13, Issue 1, February 2024)
Page(s) 1-8
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Fuzzy Nowhere Dense Set, Fuzzy Residual Set, Fuzzy Baire Set, Fuzzy Weakly Baire Space, Fuzzy Strongly Baire Space, Fuzzy Nodec Space, Fuzzy Seminormal Space, Fuzzy Globally Disconnected Space

References
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  • APA Style

    Thangaraj, G., Raji, N. (2024). On Fuzzy Baire-Separated Spaces and Related Concepts. Pure and Applied Mathematics Journal, 13(1), 1-8. https://doi.org/10.11648/j.pamj.20241301.11

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    ACS Style

    Thangaraj, G.; Raji, N. On Fuzzy Baire-Separated Spaces and Related Concepts. Pure Appl. Math. J. 2024, 13(1), 1-8. doi: 10.11648/j.pamj.20241301.11

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    AMA Style

    Thangaraj G, Raji N. On Fuzzy Baire-Separated Spaces and Related Concepts. Pure Appl Math J. 2024;13(1):1-8. doi: 10.11648/j.pamj.20241301.11

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  • @article{10.11648/j.pamj.20241301.11,
      author = {Ganesan Thangaraj and Natarajan Raji},
      title = {On Fuzzy Baire-Separated Spaces and Related Concepts},
      journal = {Pure and Applied Mathematics Journal},
      volume = {13},
      number = {1},
      pages = {1-8},
      doi = {10.11648/j.pamj.20241301.11},
      url = {https://doi.org/10.11648/j.pamj.20241301.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20241301.11},
      abstract = {In this paper, a new class of fuzzy topological spaces, namely fuzzy Baire-separated spaces is introduced in terms of fuzzy Baire sets. Several characterizations of fuzzy Baire-separated spaces are established. It is shown that fuzzy Baire sets lie between disjoint fuzzy P-sets and fuzzy Fσ- sets in a fuzzy Baire-separated space. Conditions under which fuzzy topological spaces become fuzzy Baire-separated spaces are established. Fuzzy nowhere dense sets are fuzzy closed sets in fuzzy nodec spaces and subsequently a question will arise. Which fuzzy topological spaces [other than fuzzy hyperconnected spaces, fuzzy globally disconnected spaces] have fuzzy closed sets with fuzzy nowhere denseness? For this, fuzzy topological spaces having fuzzy closed sets with fuzzy nowhere denseness are identified in this paper. It is verified that fuzzy ultraconnected spaces are non fuzzy Baire -separated spaces. The means, by which fuzzy weakly Baire space become fuzzy Baire -separated spaces and in turn fuzzy Baire - separated spaces become fuzzy seminormal spaces, are obtained. There are scope in this paper for exploring the inter-relations between fuzzy Baire spaces and Baire -separated spaces.
    },
     year = {2024}
    }
    

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    AU  - Ganesan Thangaraj
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    JF  - Pure and Applied Mathematics Journal
    JO  - Pure and Applied Mathematics Journal
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    UR  - https://doi.org/10.11648/j.pamj.20241301.11
    AB  - In this paper, a new class of fuzzy topological spaces, namely fuzzy Baire-separated spaces is introduced in terms of fuzzy Baire sets. Several characterizations of fuzzy Baire-separated spaces are established. It is shown that fuzzy Baire sets lie between disjoint fuzzy P-sets and fuzzy Fσ- sets in a fuzzy Baire-separated space. Conditions under which fuzzy topological spaces become fuzzy Baire-separated spaces are established. Fuzzy nowhere dense sets are fuzzy closed sets in fuzzy nodec spaces and subsequently a question will arise. Which fuzzy topological spaces [other than fuzzy hyperconnected spaces, fuzzy globally disconnected spaces] have fuzzy closed sets with fuzzy nowhere denseness? For this, fuzzy topological spaces having fuzzy closed sets with fuzzy nowhere denseness are identified in this paper. It is verified that fuzzy ultraconnected spaces are non fuzzy Baire -separated spaces. The means, by which fuzzy weakly Baire space become fuzzy Baire -separated spaces and in turn fuzzy Baire - separated spaces become fuzzy seminormal spaces, are obtained. There are scope in this paper for exploring the inter-relations between fuzzy Baire spaces and Baire -separated spaces.
    
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Author Information
  • Department of Mathematics, Thiruvalluvar University, Vellore, India

  • Department of Mathematics, K. M. G. College of Arts and Science, Gudiyattam, India

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