Fine Fuzzy 𝔰𝔭 Closed Sets in Fine Fuzzy Topological Spaces
R. Nandhini1, D. Amsaveni2
1R. Nandhini*, Department of Mathematics, Sri Sarada College for Women(Autonomous), Salem, India.
2D. Amsaveni, Department of Mathematics, Sri Sarada College for Women (Autonomous), Salem, India.
Manuscript received on February 06, 2020. | Revised Manuscript received on February 10, 2020. | Manuscript published on February 30, 2020. | PP: 1306-1314 | Volume-9 Issue-3, February, 2020. | Retrieval Number: C5222029320/2020©BEIESP | DOI: 10.35940/ijeat.C5222.029320
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© The Authors. Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Abstract: The main view of this article is the extended version of the fine topological space to the novel kind of space say fine fuzzy topological space which is developed by the notion called collection of quasi coincident of fuzzy sets. In this connection, fine fuzzy 𝖘𝖕closed sets are introduced and studied some features on it. Further, the relationship between fine fuzzy 𝖘𝖕closed sets with certain types of fine fuzzy closed sets are investigated and their converses need not be true are elucidated with necessary examples. Fine fuzzy 𝖘𝖕continuous function is defined as the inverse image of fine fuzzy closed set is fine fuzzy 𝖘𝖕closed and its interrelations with other types of fine fuzzy continuous functions are obtained. The reverse implication need not be true is proven with examples. Finally, the applications of fine fuzzy 𝖘𝖕continuous function are explained by using the composition.
Keywords: Fine fuzzy topological space, Fine fuzzy 𝖘𝖕closed set, Fine fuzzy continuous, Fine fuzzy 𝖘𝖕**continuous. Subject Classification Primary: 54A05, 54A10, 54A20.