Definition:Category of Open Sets/Definition 2

Definition

Let $T = \struct {S, \tau}$ be a topological space.

The category of open sets of $T$, denoted $\map {\mathbf {Ouv} } T$, is the order category of open sets of $T$ ordered by the subset relation.

Also see

• Equivalence of Definitions of Category of Open Sets

Linguistic Note

The notation $\map {\mathbf {Ouv} } T$ for the category of open sets derives from the French ouvert meaning open, in its adjectival form.