New Properties of Optimal δθ -Open and δθ-Closed Sets in Topological Spaces

Authors(1) :-Bishnupada Debnath

In this work, some conditions for dq-disconnectedness of a topological space in terms of maximal and minimal δθ -open sets and also some similar results in terms of maximal and minimal δθ -closed sets and also interrelationships between them are investigated. Generally, we find that if a space has a set which is both maximal and minimal δθ -open, then either this set is the only non-trivial δθ -open set in the space or the space is δθ-disconnected. We also obtain a result concerning a minimal δθ -open set on a subspace.

Authors and Affiliations

Bishnupada Debnath
Department of Mathematics, Tripura University, Suryamaninagar, Agartala, Tripura, India

Maximal δθ -open set, minimal δθ -open set, maximal δθ closed set, minimal δθ -closed set, δθ -disconnected

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

Publication Details

Published in : Volume 2 | Issue 5 | September-October 2017
Date of Publication : 2017-10-31
License:  This work is licensed under a Creative Commons Attribution 4.0 International License.
Page(s) : 662-666
Manuscript Number : CSEIT1725148
Publisher : Technoscience Academy

ISSN : 2456-3307

Cite This Article :

Bishnupada Debnath, "New Properties of Optimal δθ -Open and δθ-Closed Sets in Topological Spaces", International Journal of Scientific Research in Computer Science, Engineering and Information Technology (IJSRCSEIT), ISSN : 2456-3307, Volume 2, Issue 5, pp.662-666, September-October-2017.
Journal URL : http://ijsrcseit.com/CSEIT1725148

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