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

Abstract

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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