Definition:Topologically Distinguishable/Indistinguishable

Definition
Let $T = \left({X, \tau}\right)$ be a topological space.

Let $x, y \in X$.

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

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