Definition:Topologically Distinguishable/Indistinguishable

Definition
Let $T = \struct {S, \tau}$ be a topological space.

Let $x, y \in S$.

The two points $x$ and $y$ are topologically indistinguishable they are not topologically distinguishable.

That is they do not exactly the same neighborhoods:


 * $\forall U \in \tau: x \in U \iff y \in U$