# Definition:Relatively Closed Set

(Redirected from Definition:Relatively Closed)

## Definition

Let $T = \left({S, \tau}\right)$ be a topological space.

Let $A \subseteq B \subseteq S$.

### Definition 1

**$A$ is relatively closed in $B$** if and only if $A$ is closed in the relative topology of $B$.

### Definition 2

**$A$ is relatively closed in $B$** if and only if there is a closed set $C \subseteq S$ with $C \cap B = A$.