Definition:Lower Topology

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Definition

Let $T = \left({S, \preceq, \tau}\right)$ be a relational structure with topology.


Then $T$ has lower topology if and only if

$\left\{ {\complement_S\left({x^\succeq}\right): x \in S}\right\}$ is sub-basis of $T$

where $x^\succeq$ denotes the upper closure of $x$.


Sources