In this paper, we continue the discussion of T-syntopogenous spaces, which were introduced by the author in 2012. We introduce the concept of saturated T-syntopogenous structures and develop some fundamental results. Moreover, we show that the category of perfect saturated T-topogenous spaces is isomorphic to the category of I-topological spaces. Also, we deduce the notion of levels of a T-topogenuous order. We study some relationships between them. We supply an explicit formula for a T-topogenuous order inducing such these topogenuous orders.Also, we characterize number of
I-topological notions in the category of T-topogenuous spaces.
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