Upper section
From Maths
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Contents
Definition
An upper section of a preset [ilmath](A,\preceq)[/ilmath] is a subset, [ilmath]U\subseteq A[/ilmath] with the following property^{[1]}:
 [ilmath]\forall a,b\in A[(a\in U\wedge a\preceq b)\implies b\in U][/ilmath], that is:
 Given an [ilmath]a[/ilmath] and [ilmath]b[/ilmath] in [ilmath]A[/ilmath], if [ilmath]a[/ilmath] is in [ilmath]U[/ilmath] and [ilmath]a\preceq b[/ilmath] then we require [ilmath]b\in U[/ilmath]
See also
 Lower section  the dual concept to this
 [ilmath]\Uparrow[/ilmath]functor, a functor, [ilmath]:[/ilmath][ilmath]\mathrm{PRE} [/ilmath][ilmath]\leadsto[/ilmath][ilmath]\mathrm{TOP} [/ilmath] that uses this notion.
 Closely related to the Alexandroff topology
References
