Category:Definitions/Upper Sections
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This category contains definitions related to Upper Sections.
Related results can be found in Category:Upper Sections.
Let $\struct {S, \preceq}$ be an ordered set.
Let $U \subseteq S$.
Definition 1
$U$ is an upper section in $S$ if and only if:
- $\forall u \in U: \forall s \in S: u \preceq s \implies s \in U$
Definition 2
$U$ is an upper section in $S$ if and only if:
- $U^\succeq \subseteq U$
where $U^\succeq$ is the upper closure of $U$.
Definition 3
$U$ is an upper section in $S$ if and only if:
- $U^\succeq = U$
where $U^\succeq$ is the upper closure of $U$.
Pages in category "Definitions/Upper Sections"
The following 5 pages are in this category, out of 5 total.