Category:Suprema

This category contains results about Suprema in the context of Order Theory.
Definitions specific to this category can be found in Definitions/Suprema.

Let $\struct {S, \preceq}$ be an ordered set.

Let $T \subseteq S$.

An element $c \in S$ is the supremum of $T$ in $S$ if and only if:

$(1): \quad c$ is an upper bound of $T$ in $S$

$(2): \quad c \preceq d$ for all upper bounds $d$ of $T$ in $S$.

If there exists a supremum of $T$ (in $S$), we say that:

$T$ admits a supremum (in $S$) or

$T$ has a supremum (in $S$).