In topology, two points of a topological space X are topologically indistinguishable if they have exactly the same neighborhoods. That is, if x and y are points in X, and N_x is the set of all neighborhoods that contain x, and N_y is the set of all neighborhoods that contain y, then x and y are "topologically indistinguishable" if and only if N_x = N_y. (See Hausdorff's axiomatic neighborhood systems.)