Definition:Topologically Distinguishable/Indistinguishable

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Definition

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

Let $x, y \in S$.


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

That is if and only if they do not exactly the same neighborhoods:

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


Sources