Relatively open

Definition

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

Alternatively we may say given a $A\subseteq X$ the family of sets:

• $\{U_A\vert U_A=A\cap U\text{ for some }U\in\mathcal{J}\}$

are all relatively open in $A$

See also

• Open set
• Relatively closed