Introduction to Weakly b- Transitive Maps on Topological Spaces

Mohammed Nokhas Murad Kaki

doi:doi:10.11648/j.sr.20130104.11

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Introduction to Weakly b- Transitive Maps on Topological Spaces

Mohammed Nokhas Murad Kaki

Published in Science Research (Volume 1, Issue 4)

Received: 28 September 2013 Published: 10 November 2013

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Abstract

The concept of b-regular open set was introduced by N. Rajesh.. The aim of this paper is to introduce and characterize weakly b-transitive maps by using b-regular open sets and investigate some of its properties. Further, we introduce the notions of weakly b- minimal mapping. We have proved that every b-transitive map is a weakly b- transitive map but the converse not necessarily true, and that every b-minimal map is a weakly b- minimal map, but the converse not necessarily true.

Published in	Science Research (Volume 1, Issue 4)
DOI	10.11648/j.sr.20130104.11
Page(s)	59-62
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), 2013. Published by Science Publishing Group

Keywords

Weakly b- Transitive Maps, Weakly b- Minimal Functions, b- Continuous, Weakly b- Irresolute

References

[1]	S. G. Crossley and S. K. Hildebrand, Semi topological properties, Fund. Math. 74(1972)233-254.
[2]	N. Rajesh, On Weakly b-irresolute functions, No. 30(2012)
[3]	Andrijevic, D. On b-open sets, Mat. Vesnik 48 (1996), no. 1-2, 59-64
[4]	E. Ekici and M. Caldas, Slightly γ -continuous functions, Bol. Soc. Parana. Mat. (3) 22 (2004), no. 2, 63-74.
[5]	Levine N., Semi open sets and semi continuity in topological spaces. Amer. Math. Monthly. 70(1963). 36-41
[6]	J. H. Park, Strongly θ-b- continuous functions. Acta Math. Hunger., 110(4)2006, 347-350.
[7]	www.scholarpedia.org/article/Minimal_dynamical_systems
[8]	A. A. El Abik, A study of some types of mapping on topological spaces, Master's Thesis Faculty of Science. Tanta, Egypt (1997)..
[9]	Mohammed Nokhas Murad, Topologically - Transitive Maps and Minimal Systems Gen. Math. Notes,(2012) Vol. 10, No. 2, pp. 43-53 ISSN 2219-7184; Copyright © ICSRS.
[10]	Mohammed Nokhas Murad, On Some New γ-Type Maps on Topological Spaces, Journal of Mathematical Sciences: Advances and Applications (2013) Vol. (20) pp. 45-60.
[11]	Mohammed Nokhas Murad, Topologically α- Type Maps and Minimal α-Open Sets Canadian Journal on Computing in Mathematics, Natural Sciences, Engineering and Medicine (2013) Vol. 4 No. 2, pp. 177-183
[12]	Mohammed Nokhas Murad, New Types of δ-Transitive Maps, International Journal of Engineering & Technology IJET-IJENS (2012) Vol:12 No:06, pp.134-136
[13]	Keskin A. and Noiri T.. On bd-sets and associated separation axioms. Bull. Iranian Math. Soc., 35(1):179:198, 2009.
[14]	Mohammed Nokhas Murad, New Types of Transitive Functions and Minimal Systems, , International Journal of Basic & Applied Science IJBAS-IJENS Vol. 12 No. 04 (2012) pp. 53-58.

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Mohammed Nokhas Murad Kaki. (2013). Introduction to Weakly b- Transitive Maps on Topological Spaces. Science Research, 1(4), 59-62. https://doi.org/10.11648/j.sr.20130104.11

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Mohammed Nokhas Murad Kaki. Introduction to Weakly b- Transitive Maps on Topological Spaces. Sci. Res. 2013, 1(4), 59-62. doi: 10.11648/j.sr.20130104.11

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Mohammed Nokhas Murad Kaki. Introduction to Weakly b- Transitive Maps on Topological Spaces. Sci Res. 2013;1(4):59-62. doi: 10.11648/j.sr.20130104.11

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@article{10.11648/j.sr.20130104.11,
  author = {Mohammed Nokhas Murad Kaki},
  title = {Introduction to Weakly b- Transitive Maps on Topological Spaces},
  journal = {Science Research},
  volume = {1},
  number = {4},
  pages = {59-62},
  doi = {10.11648/j.sr.20130104.11},
  url = {https://doi.org/10.11648/j.sr.20130104.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sr.20130104.11},
  abstract = {The concept of b-regular open set was introduced by N. Rajesh.. The aim of this paper is to introduce and characterize weakly b-transitive maps by using b-regular open sets and investigate some of its properties. Further, we introduce the notions of weakly b- minimal mapping. We have proved that every b-transitive map is a weakly b- transitive map but the converse not necessarily true, and that every b-minimal map is a weakly b- minimal map, but the converse not necessarily true.},
 year = {2013}
}

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TY  - JOUR
T1  - Introduction to Weakly b- Transitive Maps on Topological Spaces
AU  - Mohammed Nokhas Murad Kaki
Y1  - 2013/11/10
PY  - 2013
N1  - https://doi.org/10.11648/j.sr.20130104.11
DO  - 10.11648/j.sr.20130104.11
T2  - Science Research
JF  - Science Research
JO  - Science Research
SP  - 59
EP  - 62
PB  - Science Publishing Group
SN  - 2329-0927
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AB  - The concept of b-regular open set was introduced by N. Rajesh.. The aim of this paper is to introduce and characterize weakly b-transitive maps by using b-regular open sets and investigate some of its properties. Further, we introduce the notions of weakly b- minimal mapping. We have proved that every b-transitive map is a weakly b- transitive map but the converse not necessarily true, and that every b-minimal map is a weakly b- minimal map, but the converse not necessarily true.
VL  - 1
IS  - 4
ER  -

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Author Information

Mohammed Nokhas Murad Kaki

Math Department, School of Science, Faculty of Science and Science Education, University of Sulaimani, Iraq

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Mohammed Nokhas Murad Kaki. (2013). Introduction to Weakly b- Transitive Maps on Topological Spaces. Science Research, 1(4), 59-62. https://doi.org/10.11648/j.sr.20130104.11

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ACS Style

Mohammed Nokhas Murad Kaki. Introduction to Weakly b- Transitive Maps on Topological Spaces. Sci. Res. 2013, 1(4), 59-62. doi: 10.11648/j.sr.20130104.11

Copy | Download

AMA Style

Mohammed Nokhas Murad Kaki. Introduction to Weakly b- Transitive Maps on Topological Spaces. Sci Res. 2013;1(4):59-62. doi: 10.11648/j.sr.20130104.11

Copy | Download

@article{10.11648/j.sr.20130104.11,
  author = {Mohammed Nokhas Murad Kaki},
  title = {Introduction to Weakly b- Transitive Maps on Topological Spaces},
  journal = {Science Research},
  volume = {1},
  number = {4},
  pages = {59-62},
  doi = {10.11648/j.sr.20130104.11},
  url = {https://doi.org/10.11648/j.sr.20130104.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sr.20130104.11},
  abstract = {The concept of b-regular open set was introduced by N. Rajesh.. The aim of this paper is to introduce and characterize weakly b-transitive maps by using b-regular open sets and investigate some of its properties. Further, we introduce the notions of weakly b- minimal mapping. We have proved that every b-transitive map is a weakly b- transitive map but the converse not necessarily true, and that every b-minimal map is a weakly b- minimal map, but the converse not necessarily true.},
 year = {2013}
}

Copy | Download

TY  - JOUR
T1  - Introduction to Weakly b- Transitive Maps on Topological Spaces
AU  - Mohammed Nokhas Murad Kaki
Y1  - 2013/11/10
PY  - 2013
N1  - https://doi.org/10.11648/j.sr.20130104.11
DO  - 10.11648/j.sr.20130104.11
T2  - Science Research
JF  - Science Research
JO  - Science Research
SP  - 59
EP  - 62
PB  - Science Publishing Group
SN  - 2329-0927
UR  - https://doi.org/10.11648/j.sr.20130104.11
AB  - The concept of b-regular open set was introduced by N. Rajesh.. The aim of this paper is to introduce and characterize weakly b-transitive maps by using b-regular open sets and investigate some of its properties. Further, we introduce the notions of weakly b- minimal mapping. We have proved that every b-transitive map is a weakly b- transitive map but the converse not necessarily true, and that every b-minimal map is a weakly b- minimal map, but the converse not necessarily true.
VL  - 1
IS  - 4
ER  -

Copy | Download