A subset A of a metric space M is open if every point of A is an interior point of A or, equivalently, around each point of A there exists an open ball of M which is contained in A. The open sets form the topology of M. In a topological space the open sets are, by definition, those sets in the topology.

Note that openness is a relative term and that open sets are open in another set. So [0,1) is not open in ℝ as 0 is not an interior point but [0,1) is open in [0,∞). See clopen set, closed set.