Neighborhood (mathematics)

A subset \\(N\\) of a topological space is called a neighborhood of a subset \\(K\\) if every point of \\(K\\) belongs to the interior of \\(N\ .\\) Another way of saying this is that there must be an open set \\(U\\) such that \\(K\subset U\subset N\ .\\) Thus \\(N\\) itself is not necessarily an open set.