Jan 1, 0001
Closed set
A $S$ subset of $X$ with topology $\tau$ is closed if $X \setminus S \in \tau$ (i.e. $X \setminus S$ is an open-set)
Equivalent definition
Set $F$ is closed $\iff$ contains all the point-of-closure
Jan 1, 0001
A $S$ subset of $X$ with topology $\tau$ is closed if $X \setminus S \in \tau$ (i.e. $X \setminus S$ is an open-set)
Set $F$ is closed $\iff$ contains all the point-of-closure