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Reference.org
Partially ordered space
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<p>In mathematics, a partially ordered space (or pospace) is a <a href="/facts/Topological_space/v2ut7CbK">topological space</a> X {\displaystyle X} equipped with a closed <a href="/facts/Partial_order/qb4a3FAX">partial order</a> ≤ {\displaystyle \leq } , i.e. a partial order whose graph { ( x , y ) ∈ X 2 ∣ x ≤ y } {\displaystyle \{(x,y)\in X^{2}\mid x\leq y\}} is a closed subset of X 2 {\displaystyle X^{2}} . </p><p>From pospaces, one can define dimaps, i.e. <a href="/facts/Continuous_map/sKbl02pB">continuous maps</a> between pospaces which preserve the order relation. </p>