Definition:Empty Supremum
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Definition
Let $\struct {S, \preceq}$ be an ordered set.
Then the empty supremum is the supremum $\sup \O$.
Notation
The empty supremum is sometimes denoted as $0$.
Also see
- Supremum of Empty Set is Smallest Element: the empty supremum exists if and only if $\struct {S, \preceq}$ has a smallest element.
Sources
- 1982: Peter T. Johnstone: Stone Spaces ... (previous) ... (next): Chapter $\text I$: Preliminaries, Definition $1.2$