Let \(X\) be a topological space . We call a subset \(A\subseteq M\) closed if its complement is open .

Remarks for special spaces Link to heading

Remarks for Hausdorff spaces Link to heading

Assume \(X\) is a Hausdorff space .

• Finite subsets are closed in Hausdorff spaces.

Remarks for first countable spaces Link to heading

• \(A\) is closed if and only if \(A\) contains every limit of ever converging sequence of points in \(A\).

Remarks for metric spaces Link to heading

Assume \(X\) is a metric space . Note every metric space is Hausdorff and first countable.

• Closed sets are closed regarding limits of convergent sequences on it.

See also Link to heading

• closure