More on semi quotient mappings and spaces

Abstract

A mathematical discipline assembling the topology and group is called the topological group. This discipline has very significant applications in almost all branches of natural sciences. In our arrangement operations of multiplicity and inverse on the continuity and its general forms will be discussed. The study of this weaker form of continuity with topological groups started in 1990s. Twenty-thirty years ago more interesting results relating to the discipline discussed in literature. In our paper, semi quotient mappings and spaces properties are developed by the change of topology where the notion of semi quotient topology built the interest. Results describes the more interest in our work with the contribution of extremally disconnected concept where the quotient space J/N with this topology sτQ has surprisingly moved to an s−topological group.

Keywords

• semi continuous mappings
• group structure
• quasi topological group
• semi quotient mapping

References

1. [1] E. Bohn, Semi-topological groups, The American Mathematical Monthly, 72 (9) (1965) 996- 998.
2. [2] M. S. Bosan and M. D. Khan, On quasi irresolute and semi Irr-topological groups, Afinidad, 80 (574) (2014) 1241-1252.
3. [3] M. S. Bosan, M. D. Khan and L. DR. Koˇcinac, On s-topological groups, Mathematica Moravica, 80 (2) (2014), 35-44.
4. [4] S. G. Crossley, SK. Hildebrand, Semi-topological properties, Fundamenta Mathematicae, 74 (3) (1972) 233-254.
5. [5] M. D. Khan and M. S. Bosan, A note on s-topological groups, Life Sci. J., 11 (2014) 370-374.
6. [6] JP. Lee, On semi-homeomorphisms, International Journal of Mathematics and Mathematical Sciences, 13 (1990) 129-134.
7. [7] N. Levine, Semi-open sets and semi-continuity in topological spaces, The American Mathematical Monthly, 70 (1) (1963) 36-41.
8. [8] James R Munkres, Topology, Prentice Hall Upper Saddle River, NJ, (2000).

9. [9] O. Njastad, On some classes of nearly open sets, Pacific Journal of Mathematics, 15 (3) (1965) 961-970.
10. [10] R. Noreen, M. S. Bosan and M. D. Khan, Semi-quotient mappings and spaces, Open Mathematics, 14 (1)(2016) 1014-1022.
11. [11] C. W. Patty, Foundations of topology, Jones and Bartlett Learning, (2009).
12. [12] D. JS. Robinson, A course in the theory of groups, vol. 80, Springer Science and Business Media, (2012).
13. [13] R. Shen, Remarks on products of generalized topologies, Acta Mathematica Hungarica, 124 (4) (2009) 363-369.
14. [14] A. Siab, L. DR. Koˇcinac and M. D. Khan, Irresolute-topological groups, Mathematica Moravica, 19 (1) (2015) 73-80.