topological invariant

A topological invariant of a space $X$ is a property that depends only on the topology of the space, i.e. it is shared by any topological space homeomorphic to $X$ . Common examples include compactness, connectedness, Hausdorffness, Euler characteristic, orientability, dimension, and algebraic invariants like homology, homotopy groups, and K-theory.

Properties of a space depending on an extra structure such as a metric (i.e. volume, curvature, symplectic invariants) typically are not topological invariants, though sometimes there are useful interpretations of topological invariants which seem to depend on extra information like a metric (for example, the Gauss-Bonnet theorem).