Relatively open

Definition

Given a subspace [ilmath]Y\subset X[/ilmath] of a topological space [ilmath](X,\mathcal{J})[/ilmath], the open sets of [ilmath](Y,\mathcal{J}_\text{subspace})[/ilmath] are said to be relatively open in [ilmath]X[/ilmath]

That (more generally) given a [ilmath]A\subseteq X[/ilmath] the family of sets:

• [ilmath]\{U_A\vert U_A=A\cap U\text{ for some }U\in\mathcal{J}\}[/ilmath]

are all relatively open

See also

• Open set
• Relatively closed