Initial and the final T -topogenous structures

Abstract

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.