Bottom is Compact
Jump to navigation
Jump to search
Theorem
Let $L$ be a bounded below ordered set.
Then $\bot$ is a compact element
where $\bot$ is the smallest element in $L$.
Proof
By Bottom is Way Below Any Element:
- $\bot \ll \bot$
where $\ll$ denotes the way below relation.
Hence $\bot$ is a compact element.
$\blacksquare$
Sources
- Mizar article WAYBEL_3:15