\begin{definition}[Definition:Lower Topology]
Let $T = \left({S, \preceq, \tau}\right)$ be a relational structure with topology.
Then $T$ has '''lower topology''' {{iff}}
:$\left\{ {\complement_S\left({x^\succeq}\right): x \in S}\right\}$ is sub-basis of $T$
where $x^\succeq$ denotes the upper closure of $x$.
\end{definition}