On Fuzzy Semi-P-spaces and Related Concepts

Ganesan Thangaraj; Ayyavu Vinothkumar

doi:doi:10.11648/j.pamj.20221101.12

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On Fuzzy Semi-P-spaces and Related Concepts

Ganesan Thangaraj, Ayyavu Vinothkumar

Published in Pure and Applied Mathematics Journal (Volume 11, Issue 1)

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 G_δ-sets and fuzzy F_σ-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 G_δ-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), 2024. Published by Science Publishing Group

Keywords

Fuzzy G_δ-set, Fuzzy F_σ-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.
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[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.
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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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TY  - JOUR
T1  - On Fuzzy Semi-P-spaces and Related Concepts
AU  - Ganesan Thangaraj
AU  - Ayyavu Vinothkumar
Y1  - 2022/03/09
PY  - 2022
N1  - https://doi.org/10.11648/j.pamj.20221101.12
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
SP  - 20
EP  - 27
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
IS  - 1
ER  -

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Author Information

Ganesan Thangaraj

Department of Mathematics, Thiruvalluvar University, Vellore, India
Ayyavu Vinothkumar

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

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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

Copy | Download

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

Copy | Download

@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}
}

Copy | Download

TY  - JOUR
T1  - On Fuzzy Semi-P-spaces and Related Concepts
AU  - Ganesan Thangaraj
AU  - Ayyavu Vinothkumar
Y1  - 2022/03/09
PY  - 2022
N1  - https://doi.org/10.11648/j.pamj.20221101.12
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
SP  - 20
EP  - 27
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
IS  - 1
ER  -

Copy | Download