Definition:Topologically Distinguishable/Indistinguishable
< Definition:Topologically Distinguishable(Redirected from Definition:Topologically 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
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): topologically distinguishable