Local $T_0$ and $T_1$ quantale-valued preordered spaces

In this paper, we characterize explicitly the separation properties $T_0$ and $T_1$ at a point p in the topological category of quantale-valued preordered spaces and investigate how these characterizations are related. Moreover, we prove that local $T_0$ and $T_1$ quantale-valued preordered spaces are hereditary and productive.

Keywords:

Topological category, quantale-valued preorder local $T_0$ objects, local $T_1$ objects,

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