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.
| Published in | Pure and Applied Mathematics Journal (Volume 13, Issue 1) |
| DOI | 10.11648/j.pamj.20241301.11 |
| Page(s) | 1-8 |
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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. |
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Copyright © The Author(s), 2024. Published by Science Publishing Group |
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
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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
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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Download@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}
}
TY - JOUR T1 - On Fuzzy Baire-Separated Spaces and Related Concepts AU - Ganesan Thangaraj AU - Natarajan Raji Y1 - 2024/03/20 PY - 2024 N1 - https://doi.org/10.11648/j.pamj.20241301.11 DO - 10.11648/j.pamj.20241301.11 T2 - Pure and Applied Mathematics Journal JF - Pure and Applied Mathematics Journal JO - Pure and Applied Mathematics Journal SP - 1 EP - 8 PB - Science Publishing Group SN - 2326-9812 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. VL - 13 IS - 1 ER -
Department of Mathematics, Thiruvalluvar University, Vellore, India
Department of Mathematics, K. M. G. College of Arts and Science, Gudiyattam, India
