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.)