Initial and the final T-topogenous structures

Article type: Research Article

Authors: Hashem, Khaled A.^*

Affiliations: Department of Mathematics, Faculty of Science, Benha University, Benha, Egypt

Correspondence: [*] Corresponding author. Khaled A. Hashem, Department ofMathematics, Faculty of Science, Benha University, Benha, Egypt. E-mails: khaledahashem@yahoo.com; khaled.hashem@fsc.bu.edu.eg

Abstract: This paper is devoted to study the initial and the final T-topogenous structures of the T-topogenous spaces, defined by the author in 2012. In this manuscript, we show that all initial (final) lifts in the category of T-topogenous spaces and the initial (final) T-topogenous structures exist. We introduce characterizations of the initial T-topogenous structures as special initial T-topogenous structures. The subspaces and product spaces of these T-topogenous spaces can be also characterized. Moreover, we show that the I-topology associated to the initial T-topogenous structure of a family of T-topogenous spaces coincides with the initial I-topology of the family of I-topologies associated to these T-topogenous spaces.

Keywords: I-topological spaces, T-topogenous spaces, initial and final T-topogenous structures

DOI: 10.3233/IFS-141452

Journal: Journal of Intelligent & Fuzzy Systems, vol. 29, no. 4, pp. 1331-1342, 2015