Volume 7, Issue 1, February 2018, Page: 1-5
The Study of the Concept of Q*Compact Spaces
Ibrahim Bassi, Department of Mathematics, Federal University, Lafia, Nigeria
Yakubu Gabriel, Department of Mathematics, Shepherd’s International College, Akwanga, Nigeria
Onuk Oji Galadima, Department of Physics, Federal University, Gashua, Nigeria
Received: Oct. 24, 2017;       Accepted: Nov. 15, 2017;       Published: Feb. 2, 2018
DOI: 10.11648/j.pamj.20180701.11      View  1625      Downloads  92
Abstract
The aim of this research is to extend the new type of compact spaces called Q* compact spaces, study its properties and generate new results of the space. It investigate the Q*-compactness of topological spaces with separable, Q*-metrizable, Q*-Hausdorff, homeomorphic, connected and finite intersection properties. The closed interval [0, 1] is Q* compact. So, it is deduced that the closed interval [0, 1] is Q*-compact. For example, if (X, τ) = ℝ and A = (0, ∞) then A is not Q*-compact. A subset S of ℝ is Q*-compact. Also, if (X, τ) is a Q*-compact metrizable space. Then (X, τ) is separable. (Y, τ1) is Q*-compact and metrizable if f is a continuous mapping of a Q*-compact metric space (X, d) onto a Q*-Hausdorff space (Y, τ1). An infinite subset of a Q*-compact space must have a limit point. The continuous mapping of a Q*-compact space has a greatest element and a least element. Eleven theorems were considered and their results were presented accordingly.
Keywords
Topological Paces, Semi Compact Spaces, Q*O Compact Space
To cite this article
Ibrahim Bassi, Yakubu Gabriel, Onuk Oji Galadima, The Study of the Concept of Q*Compact Spaces, Pure and Applied Mathematics Journal. Vol. 7, No. 1, 2018, pp. 1-5. doi: 10.11648/j.pamj.20180701.11
Copyright
Copyright © 2018 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Reference
[1]
P. Padma, S. Udayakumar, (January 2015) On Q*O Compact spaces, Journal of Progressive Research in Mathematics (JPRM) ISSN: 2395-0218 Volume 1, Issue 1.
[2]
P. Padma, S. Udayakumar, (January 2015) On Q*s - regular spaces, Journal of Progressive Research in Mathematics (JPRM) ISSN: 2395-0218 Volume 1, Issue 1.
[3]
P. Padma, K. Chandrasekhararao and S. Udayakumar, (2013) “Pairwise SC compact spaces”, International Journal of Analysis and Applications, Volume 2, Number 2, 162-172.
[4]
M. Murugalingam and N. Laliltha, ( 2010) “Q star sets”, Bulletin of pure and applied Sciences, Volume 29E Issue 2 p. 369-376.
[5]
M. Murugalingam and N. Laliltha, (2011) “Properties of Q* sets”, Bulletin of pure and applied Sciences, Volume 3E Issue 2 p. 267-277.
[6]
P. Padma and S. Udayakumar, (2011) “Pairwise Q* separation axioms in bitopological spaces” International Journal of Mathematical Achieve – 3 (12), 2012, 4959-4971.
[7]
P. Padma and S. Udayakumar, (Jul - Aug 2012) “τ1τ2- Q* continuous maps in bitopological spaces” Asian Journal of Current Engineering and Mathematics, 1:4, 227-229.
[8]
Sidney A. Morris, (2011) “Topology without Tears”, version of January 2 2011. P. 155-167.
[9]
Tom Benidec, Chris Best and Michael Bliss, (2007) “Introduction to Topology”, Renzo’s Math 470, Winter, p. 24-55.
[10]
Kannan. K., (2009) “Contribution to the study of some generalized closed sets in bitopological spaces, (Ph.D Thesis).
[11]
V. K. Sharma: (1990) A study of some separation and covering axioms in topological and bitopological spaces. Ph. D. Thesis, Meerut Univ.
Browse journals by subject