Definition:Well Inside Relation
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Definition
Let $L = \struct {S, \vee, \wedge, \preceq}$ be a distributive lattice with greatest element $\top$ and smallest element $\bot$.
Let $a, b \in S : a \preceq b$.
Then $a$ is said to be well inside $b$, denoted $a \eqslantless b$, if and only if:
- $\exists c \in S : a \wedge c = \bot$ and $b \vee c = \top$
Also see
- Results about Well Inside Relation can be found here.
Sources
- 1982: Peter T. Johnstone: Stone Spaces: Chapter $\text {III}$: Compact Hausdorff Spaces, $\S1.1$