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
- 1980: G. Gierz, K.H. Hofmann, K. Keimel, J.D. Lawson, M.W. Mislove and D.S. Scott: A Compendium of Continuous Lattices
- Mizar article WAYBEL19:def 1