International Journal of Nonlinear Analysis and Applications
Feeble regular and feeble normal spaces in $\alpha$-topological spaces using graph
Document Type : Research Paper
Authors
Department of Mathematics, College of Education for Pure Sciences (Ibn Al-Haitham), University of Baghdad, Iraq
Abstract
This paper introduces some properties of separation axioms called $\alpha$ -feeble regular and $\alpha$ -feeble normal spaces (which are weaker than the usual axioms) by using elements of graph which are the essential parts of our $\alpha$ -topological spaces that we study them. Also, it presents some dependent concepts and studies their properties and some relationships between them.
Keywords
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[2] C. Dorsett, Feebly separation axioms, the feebly induced topology and separation axioms and the feebly induced topology, J . Karadeniz Univ. Math. J. 8 (1985) 43–54.
[3] M. C. Gemignani, Elementary Topology, Buffalo. State University of New York, 1972.
[4] F. Harary, Graph Theory, Addison–Wesley, Reading, MA, 1969.
[5] N. Levine, Generalized closed sets in topology, Rend. Circ. Math. Palermo, 19 (1970) 89–96.
[6] S. N. Maheswari and U. Tapi, On feebly ρ-spaces, An. Univ Timisoara. Ser. Stiint Math. 16 (1978) 173–177.
[7] B. K. Mahmoud and Y. Y. Yousif, Cutpoints and separations in connected α-topological spaces, Iraq J. Sci., accepted (2020).
[8] B. K. Mahmoud and Y. Y. Yousif, Compatibility and edge spaces in α-topological spaces, to appear.
[9] B. K. Mahmoud and Y. Y. Yousif, Feeble Hausdorff spaces in α-topological spaces using graph, accepted in IOP Conference (2021).
[10] M. Mrsevic and I. L. Reilly, Separation properties of a topological spaces and its associatted topology of subsets, Belgrade. Kyungpook. Math. J. 33(1) (1993) 75–86.
[11] O. Njastad, On some classes of nearly open sets, Pacific J. Math. 15 (1965) 961–970.
[12] S. J. Radhi, M. A. Abdlhusein and A. E. Hashoosh, The arrow domination in graphs, Int. J. Nonlenear Anal. Appl. 12(1) (2021) 473–480.
[13] T. C. K. Raman, V. Kumari and M. K. Sharma, α-generalized and α∗-separation axioms for topological spaces, IOSR J. Math. 10(3) (2014) 32–36 .
[14] U. Tapi, Feebly Regular and Feebly Normal Spaces, J. Indain Acad. Math., 9 (1987) 104–109.
[15] U. Tapi, On Pairwise Feebly Ro- Spaces, Belgrade. Kyungpook. Math. J., 30 (1990) 81–85.
[16] A. Vella, A Fundamentally Topological Perspective on Graph Theory, Ph. D. Thesis, Waterloo, Ontaio, Canada,2005.
[17] S. Willard, General topology, London-Don Mills. Addison-Wesley Publishing Co. Reading Mass. Ontaio, 1970.
[2] C. Dorsett, Feebly separation axioms, the feebly induced topology and separation axioms and the feebly induced topology, J . Karadeniz Univ. Math. J. 8 (1985) 43–54.
[3] M. C. Gemignani, Elementary Topology, Buffalo. State University of New York, 1972.
[4] F. Harary, Graph Theory, Addison–Wesley, Reading, MA, 1969.
[5] N. Levine, Generalized closed sets in topology, Rend. Circ. Math. Palermo, 19 (1970) 89–96.
[6] S. N. Maheswari and U. Tapi, On feebly ρ-spaces, An. Univ Timisoara. Ser. Stiint Math. 16 (1978) 173–177.
[7] B. K. Mahmoud and Y. Y. Yousif, Cutpoints and separations in connected α-topological spaces, Iraq J. Sci., accepted (2020).
[8] B. K. Mahmoud and Y. Y. Yousif, Compatibility and edge spaces in α-topological spaces, to appear.
[9] B. K. Mahmoud and Y. Y. Yousif, Feeble Hausdorff spaces in α-topological spaces using graph, accepted in IOP Conference (2021).
[10] M. Mrsevic and I. L. Reilly, Separation properties of a topological spaces and its associatted topology of subsets, Belgrade. Kyungpook. Math. J. 33(1) (1993) 75–86.
[11] O. Njastad, On some classes of nearly open sets, Pacific J. Math. 15 (1965) 961–970.
[12] S. J. Radhi, M. A. Abdlhusein and A. E. Hashoosh, The arrow domination in graphs, Int. J. Nonlenear Anal. Appl. 12(1) (2021) 473–480.
[13] T. C. K. Raman, V. Kumari and M. K. Sharma, α-generalized and α∗-separation axioms for topological spaces, IOSR J. Math. 10(3) (2014) 32–36 .
[14] U. Tapi, Feebly Regular and Feebly Normal Spaces, J. Indain Acad. Math., 9 (1987) 104–109.
[15] U. Tapi, On Pairwise Feebly Ro- Spaces, Belgrade. Kyungpook. Math. J., 30 (1990) 81–85.
[16] A. Vella, A Fundamentally Topological Perspective on Graph Theory, Ph. D. Thesis, Waterloo, Ontaio, Canada,2005.
[17] S. Willard, General topology, London-Don Mills. Addison-Wesley Publishing Co. Reading Mass. Ontaio, 1970.
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Volume 12, Issue 2
November 2021Pages 415-423
- Receive Date: 19 February 2021
- Revise Date: 21 March 2021
- Accept Date: 30 April 2021