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On Fuzzy Semi-P-spaces and Related Concepts

Received: 17 January 2022     Accepted: 23 February 2022     Published: 9 March 2022
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Abstract

In this paper the notion of fuzzy semi-P-spaces is introduced and studied. It is established that the class of fuzzy semi-P-spaces lies between the classes of fuzzy-P-spaces and fuzzy almost-P-spaces. It is established that fuzzy fuzzy σ-nowhere dense sets in fuzzy Semi-P-spaces are fuzzy Semi-closed sets and fuzzy Gδ-sets and fuzzy Fσ-sets are fuzzy σ-nowhere sets in fuzzy hyperconnected and semi-P-spaces are fuzzy dense sets. Also it is found that fuzzy residual sets in fuzzy globally disconnected and fuzzy Semi-P-spaces are fuzzy semi-open sets and fuzzy Gδ-sets in fuzzy perfectly disconnected and fuzzy Semi-P-spaces are fuzzy pre-open sets. Also it is established that fuzzy hyperconnected and semi-P-spaces are fuzzy irresolvable spaces. The conditions for fuzzy semi- P-spaces to become fuzzy σ-Baire spaces and fuzzy Baire spaces are obtained. The conditions for the fuzzy semi-P-spaces to become fuzzy strongly irresolvable spaces are also obtained in this paper.

Published in Pure and Applied Mathematics Journal (Volume 11, Issue 1)
DOI 10.11648/j.pamj.20221101.12
Page(s) 20-27
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), 2022. Published by Science Publishing Group

Keywords

Fuzzy Gδ-set, Fuzzy Fσ-set, Fuzzy Semi-open Set, Fuzzy Almost P-space, Fuzzy σ-Baire Space, Fuzzy Baire Space, Fuzzy Perfectly Disconnected Space

References
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[7] G. Thangaraj and G. Balasubramanian, On Fuzzy Basically Disconnected Spaces, J. Fuzzy Math., 9 (1) (2001), 103–110.
[8] G. Thangaraj and G. Balasubramanian, On Somewhat Fuzzy Continuous Functions, J. Fuzzy Math, 11 (2) (2003), 725–736.
[9] G. Thangaraj, Resolvability and irresolvability in fuzzy topological spaces, News Bull. Cal. Math. Soc., 31 (4-6) (2008), 11 − 14.
[10] G. Thangaraj and G. Balasubramanian, On Fuzzy Resolvable and Fuzzy Irresolvable Spaces, Fuzzy Sets, Rough Sets and Multivalued Operations and Appl., Vol. 1, No. 2 (2009), 173–180.
[11] G. Thangaraj and S. Anjalmose, Some remarks on Fuzzy Baire Spaces, Scientia Magna, Vol. 9, No 1. (2013), 1–6.
[12] G. Thangaraj and E. Poongothai, On Fuzzy σ-Baire Spaces, Int. J.Fuzzy Math. Sys., 3 (4) (2013), 275–283.
[13] G. Thangaraj and C. Anbazhagan, On Fuzzy Almost P-spaces, Inter. J. Innov. Sci., Engin. & Tech, Vol. 2, No. 4 (2015), 389–407.
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[18] G. Thangaraj and S. Muruganantham, A Note on Fuzzy Perfectly Disconnected Spaces, Adv. Fuzzy Math., Vol. 13, No. 1 (2018), 59–70.
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  • APA Style

    Ganesan Thangaraj, Ayyavu Vinothkumar. (2022). On Fuzzy Semi-P-spaces and Related Concepts. Pure and Applied Mathematics Journal, 11(1), 20-27. https://doi.org/10.11648/j.pamj.20221101.12

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    ACS Style

    Ganesan Thangaraj; Ayyavu Vinothkumar. On Fuzzy Semi-P-spaces and Related Concepts. Pure Appl. Math. J. 2022, 11(1), 20-27. doi: 10.11648/j.pamj.20221101.12

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    AMA Style

    Ganesan Thangaraj, Ayyavu Vinothkumar. On Fuzzy Semi-P-spaces and Related Concepts. Pure Appl Math J. 2022;11(1):20-27. doi: 10.11648/j.pamj.20221101.12

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  • @article{10.11648/j.pamj.20221101.12,
      author = {Ganesan Thangaraj and Ayyavu Vinothkumar},
      title = {On Fuzzy Semi-P-spaces and Related Concepts},
      journal = {Pure and Applied Mathematics Journal},
      volume = {11},
      number = {1},
      pages = {20-27},
      doi = {10.11648/j.pamj.20221101.12},
      url = {https://doi.org/10.11648/j.pamj.20221101.12},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20221101.12},
      abstract = {In this paper the notion of fuzzy semi-P-spaces is introduced and studied. It is established that the class of fuzzy semi-P-spaces lies between the classes of fuzzy-P-spaces and fuzzy almost-P-spaces. It is established that fuzzy fuzzy σ-nowhere dense sets in fuzzy Semi-P-spaces are fuzzy Semi-closed sets and fuzzy Gδ-sets and fuzzy Fσ-sets are fuzzy σ-nowhere sets in fuzzy hyperconnected and semi-P-spaces are fuzzy dense sets. Also it is found that fuzzy residual sets in fuzzy globally disconnected and fuzzy Semi-P-spaces are fuzzy semi-open sets and fuzzy Gδ-sets in fuzzy perfectly disconnected and fuzzy Semi-P-spaces are fuzzy pre-open sets. Also it is established that fuzzy hyperconnected and semi-P-spaces are fuzzy irresolvable spaces. The conditions for fuzzy semi- P-spaces to become fuzzy σ-Baire spaces and fuzzy Baire spaces are obtained. The conditions for the fuzzy semi-P-spaces to become fuzzy strongly irresolvable spaces are also obtained in this paper.},
     year = {2022}
    }
    

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    T1  - On Fuzzy Semi-P-spaces and Related Concepts
    AU  - Ganesan Thangaraj
    AU  - Ayyavu Vinothkumar
    Y1  - 2022/03/09
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    DO  - 10.11648/j.pamj.20221101.12
    T2  - Pure and Applied Mathematics Journal
    JF  - Pure and Applied Mathematics Journal
    JO  - Pure and Applied Mathematics Journal
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    PB  - Science Publishing Group
    SN  - 2326-9812
    UR  - https://doi.org/10.11648/j.pamj.20221101.12
    AB  - In this paper the notion of fuzzy semi-P-spaces is introduced and studied. It is established that the class of fuzzy semi-P-spaces lies between the classes of fuzzy-P-spaces and fuzzy almost-P-spaces. It is established that fuzzy fuzzy σ-nowhere dense sets in fuzzy Semi-P-spaces are fuzzy Semi-closed sets and fuzzy Gδ-sets and fuzzy Fσ-sets are fuzzy σ-nowhere sets in fuzzy hyperconnected and semi-P-spaces are fuzzy dense sets. Also it is found that fuzzy residual sets in fuzzy globally disconnected and fuzzy Semi-P-spaces are fuzzy semi-open sets and fuzzy Gδ-sets in fuzzy perfectly disconnected and fuzzy Semi-P-spaces are fuzzy pre-open sets. Also it is established that fuzzy hyperconnected and semi-P-spaces are fuzzy irresolvable spaces. The conditions for fuzzy semi- P-spaces to become fuzzy σ-Baire spaces and fuzzy Baire spaces are obtained. The conditions for the fuzzy semi-P-spaces to become fuzzy strongly irresolvable spaces are also obtained in this paper.
    VL  - 11
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Author Information
  • Department of Mathematics, Thiruvalluvar University, Vellore, India

  • Research Scholar, Department of Mathematics, Thiruvalluvar University, Vellore, India

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