In topology, a subset of a topological space is called relatively open (or open in the subspace topology) if it is an open set when considered as a subspace of the larger space.

For example, consider the real numbers with the standard topology (where open sets are defined as unions of intervals), and let X be a subset of the real numbers. A subset of X is relatively open in X if it is an open set in the topological space consisting of X with the subspace topology. This means that the subset is the union of some collection of open intervals in X, where open intervals are defined using the standard topology of the real numbers.

For example, if X is the interval [0, 1], then the subset (0, 1) is relatively open in X, but the subset [0, 1) is not relatively open in X, because it is not an open set in the subspace topology.