Definition:Compact Closure
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Definition
Let $L = \struct{S, \preceq}$ be an ordered set.
Let $x \in S$.
Then compact closure of $x$, denoted $x^{\mathrm{compact}}$, is defined by
- $x^{\mathrm{compact}} := \leftset {y \in S: y \preceq x \land y}$ is compact$\rightset{}$
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 WAYBEL_8:def 2