In mathematics, a partially ordered space[1] (or pospace) is a topological space
equipped with a closed partial order
, i.e. a partial order whose graph
From pospaces, one can define dimaps, i.e. continuous maps between pospaces which preserve the order relation.
equipped with a partial order
, the following are equivalent: The order topology is a special case of this definition, since a total order is also a partial order.
Every pospace is a Hausdorff space.
as the partial order, this definition becomes the definition of a Hausdorff space.
are nets converging to x and y, respectively, such that
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