η-Open Sets in Topological Spaces
D. Subbulakshmi1, K. Sumathi2, K. Indirani3
1D. Subbulakshmi, Assistant Professor, Department of Mathematics RathnavelSubramaniam College of Arts and Science, Coimbatore, India.
2Dr. K. Sumathi,Department of Mathematics,PSGR Krishnammal College for Women, Coimbatore – India.
3Dr. K. Indirani, Department of Mathematics,Nirmala College for Women, Coimbatore – India.
Manuscript received on 02 October 2019 | Revised Manuscript received on 13 October 2019 | Manuscript Published on 29 June 2020 | PP: 276-282 | Volume-8 Issue-10S2 August 2019 | Retrieval Number: J104908810S19/2019©BEIESP | DOI: 10.35940/ijitee.J1049.08810S19
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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: In this paper a new class of open sets in a topological space called η-open sets is defined and the inclusive relationship of this set with the other existing sets like semi open, pre-open, α-open, r-open sets are discussed.In addition to this the concept of η-interior, η-closure, η-boundary, η-exterior, η-derived, η-border, η-neighbourhood, η-dense, η-residual are also introduced.
Keywords: η-open, η-closed, η-interior, η-closure, η-boundary, η-exterior, η-derived, η-border, η-neighbourhood, η-dense, η-residual.
Scope of the Article: Applied Mathematics and Mechanics