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New Notion of open Sets in Topological Spaces

by Bishnupada Debnath
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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 177 - Number 3
Year of Publication: 2017
Authors: Bishnupada Debnath
10.5120/ijca2017915693

Bishnupada Debnath . New Notion of open Sets in Topological Spaces. International Journal of Computer Applications. 177, 3 ( Nov 2017), 33-36. DOI=10.5120/ijca2017915693

@article{ 10.5120/ijca2017915693,
author = { Bishnupada Debnath },
title = { New Notion of open Sets in Topological Spaces },
journal = { International Journal of Computer Applications },
issue_date = { Nov 2017 },
volume = { 177 },
number = { 3 },
month = { Nov },
year = { 2017 },
issn = { 0975-8887 },
pages = { 33-36 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume177/number3/28608-2017915693/ },
doi = { 10.5120/ijca2017915693 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-07T00:44:53.499285+05:30
%A Bishnupada Debnath
%T New Notion of open Sets in Topological Spaces
%J International Journal of Computer Applications
%@ 0975-8887
%V 177
%N 3
%P 33-36
%D 2017
%I Foundation of Computer Science (FCS), NY, USA
Abstract

Nakaoka and Oda ([1] and [2]) initiated the notion of maximal open (resp. minimal closed) sets in topological spaces. Thereafter, in 2005, Cao,Ganster, Reilly and Steiner [4] introduced δθ-open (resp. δθ-closed) sets in general topology. In the present work, the author introduces new classes of open and closed sets called maximal δθ-open sets, minimal δθ-open sets, maximal δθ-closed sets, minimal δθ-closed sets, δθ-semi maximal open and δθ-semi minimal closed and investigate some of their fundamental properties.

References
  1. F. Nakaoka and N. Oda, “Some applications of minimal open sets”, Int. J. Math. Math. Sci. 27 (2001), no. 8, 471- 476.
  2. F. Nakaoka and N. Oda, “Some properties of maximal open sets”, Int. J. Math. Math. Sci. 21(2003), 1331- 1340.
  3. N. V. Velicko, “H-closed topological spaces”, Mat. Sb. (N.S.) 70(112) (1966), 98-112.
  4. J. Cao, M. Ganster, I. Reilly and M. Steiner, “(-closure,(-closure and Generalized Closed sets”, Applied General Topology, Vol. 6 (2005), No. 1, 79-86.
  5. N. Levine, Generalized closed sets in topology. Rendiconti del Circ. Math. Di Palermo, Vol. 19(1970) , 89-96. “Amer. Math. Monthly”, 70, 36 – 41 (1963).
Index Terms

Computer Science
Information Sciences

Keywords

δ-open θ-open maximal (resp. minimal) δθ-open maximal (resp. minimal) δθ-closed δθ-semi maximal open and δθ-semi minimal closed sets.

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