The Study of the Concept of Q*Compact Spaces

Ibrahim Bassi; Yakubu Gabriel; Onuk Oji Galadima

doi:doi:10.11648/j.pamj.20180701.11

| Peer-Reviewed

The Study of the Concept of Q*Compact Spaces

Ibrahim Bassi, Yakubu Gabriel, Onuk Oji Galadima

Published in Pure and Applied Mathematics Journal (Volume 7, Issue 1)

Received: 24 October 2017 Accepted: 15 November 2017 Published: 2 February 2018

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

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.

Published in	Pure and Applied Mathematics Journal (Volume 7, Issue 1)
DOI	10.11648/j.pamj.20180701.11
Page(s)	1-5
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2018. Published by Science Publishing Group

Keywords

Topological Paces, Semi Compact Spaces, Q*O Compact Space

References

[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.

Cite This Article

Plain Text BibTeX RIS

APA Style

Ibrahim Bassi, Yakubu Gabriel, Onuk Oji Galadima. (2018). The Study of the Concept of Q*Compact Spaces. Pure and Applied Mathematics Journal, 7(1), 1-5. https://doi.org/10.11648/j.pamj.20180701.11

Copy | Download

ACS Style

Ibrahim Bassi; Yakubu Gabriel; Onuk Oji Galadima. The Study of the Concept of Q*Compact Spaces. Pure Appl. Math. J. 2018, 7(1), 1-5. doi: 10.11648/j.pamj.20180701.11

Copy | Download

AMA Style

Ibrahim Bassi, Yakubu Gabriel, Onuk Oji Galadima. The Study of the Concept of Q*Compact Spaces. Pure Appl Math J. 2018;7(1):1-5. doi: 10.11648/j.pamj.20180701.11

Copy | Download

@article{10.11648/j.pamj.20180701.11,
  author = {Ibrahim Bassi and Yakubu Gabriel and Onuk Oji Galadima},
  title = {The Study of the Concept of Q*Compact Spaces},
  journal = {Pure and Applied Mathematics Journal},
  volume = {7},
  number = {1},
  pages = {1-5},
  doi = {10.11648/j.pamj.20180701.11},
  url = {https://doi.org/10.11648/j.pamj.20180701.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20180701.11},
  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.},
 year = {2018}
}

Copy | Download

TY  - JOUR
T1  - The Study of the Concept of Q*Compact Spaces
AU  - Ibrahim Bassi
AU  - Yakubu Gabriel
AU  - Onuk Oji Galadima
Y1  - 2018/02/02
PY  - 2018
N1  - https://doi.org/10.11648/j.pamj.20180701.11
DO  - 10.11648/j.pamj.20180701.11
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 1
EP  - 5
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20180701.11
AB  - 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.
VL  - 7
IS  - 1
ER  -

Copy | Download

Author Information

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

Download PDF

Sections

Plain Text BibTeX RIS

APA Style

Ibrahim Bassi, Yakubu Gabriel, Onuk Oji Galadima. (2018). The Study of the Concept of Q*Compact Spaces. Pure and Applied Mathematics Journal, 7(1), 1-5. https://doi.org/10.11648/j.pamj.20180701.11

Copy | Download

ACS Style

Ibrahim Bassi; Yakubu Gabriel; Onuk Oji Galadima. The Study of the Concept of Q*Compact Spaces. Pure Appl. Math. J. 2018, 7(1), 1-5. doi: 10.11648/j.pamj.20180701.11

Copy | Download

AMA Style

Ibrahim Bassi, Yakubu Gabriel, Onuk Oji Galadima. The Study of the Concept of Q*Compact Spaces. Pure Appl Math J. 2018;7(1):1-5. doi: 10.11648/j.pamj.20180701.11

Copy | Download

@article{10.11648/j.pamj.20180701.11,
  author = {Ibrahim Bassi and Yakubu Gabriel and Onuk Oji Galadima},
  title = {The Study of the Concept of Q*Compact Spaces},
  journal = {Pure and Applied Mathematics Journal},
  volume = {7},
  number = {1},
  pages = {1-5},
  doi = {10.11648/j.pamj.20180701.11},
  url = {https://doi.org/10.11648/j.pamj.20180701.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20180701.11},
  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.},
 year = {2018}
}

Copy | Download

TY  - JOUR
T1  - The Study of the Concept of Q*Compact Spaces
AU  - Ibrahim Bassi
AU  - Yakubu Gabriel
AU  - Onuk Oji Galadima
Y1  - 2018/02/02
PY  - 2018
N1  - https://doi.org/10.11648/j.pamj.20180701.11
DO  - 10.11648/j.pamj.20180701.11
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 1
EP  - 5
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20180701.11
AB  - 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.
VL  - 7
IS  - 1
ER  -

Copy | Download