Research Article
New Notion of open Sets in Topological Spaces
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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
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| Volume 177 - Issue 3 |
| Published: Nov 2017 |
| Authors: Bishnupada Debnath |
10.5120/ijca2017915693
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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 },
year = { 2017 },
volume = { 177 },
number = { 3 },
pages = { 33-36 },
doi = { 10.5120/ijca2017915693 },
publisher = { Foundation of Computer Science (FCS), NY, USA }
}
%0 Journal Article
%D 2017
%A Bishnupada Debnath
%T New Notion of open Sets in Topological Spaces%T
%J International Journal of Computer Applications
%V 177
%N 3
%P 33-36
%R 10.5120/ijca2017915693
%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
- F. Nakaoka and N. Oda, “Some applications of minimal open sets”, Int. J. Math. Math. Sci. 27 (2001), no. 8, 471- 476.
- F. Nakaoka and N. Oda, “Some properties of maximal open sets”, Int. J. Math. Math. Sci. 21(2003), 1331- 1340.
- N. V. Velicko, “H-closed topological spaces”, Mat. Sb. (N.S.) 70(112) (1966), 98-112.
- 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.
- 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).
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