Open neighborhood: An open neighborhood of a point in a topological space is a subset of the space that contains an open set containing the point.

Closed neighborhood: A closed neighborhood of a point in a topological space is a subset of the space that contains a closed set containing the point.

Neighborhood basis: A neighborhood basis at a point in a topological space is a collection of open sets such that every open set containing the point contains at least one element of the collection.

Neighborhood axiom: A topological space satisfies the neighborhood axiom if for every point in the space and every open set containing the point, there exists a neighborhood of the point contained in the open set.

Neighborhood theorem: The neighborhood theorem states that in a topological space, every point has a neighborhood basis consisting of open sets.