In topological spaces the elements of the respective topologies are called open.

Characterizations Link to heading

• \(A\) open if and only if \(A=\Int A\).
• \(A\) open if and only if every point of \(A\) has a neighbourhood contained in \(A\).
• \(A\) is open if and only if it contains none of its boundary points.
• \(A\) is open if it satisfies the basis criterion .

Characterizations in first countable spaces Link to heading

• \(A\) is open if and only if every sequence in \(A\) converging to a point of \(A\) is eventually in \(A\).

See also Link to heading

• open sets in metric spaces
• closed set
• interior