User:Leigh.Samphier/Topology/T1 Space need not be Sober

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Theorem

Let $\struct{S, \tau}$ be a $T_1$ space.

Then:

$\struct{S, \tau}$ need not be a sober space

Proof

$\blacksquare$

Also see

• User:Leigh.Samphier/Topology/Sober Space need not be T1

Sources

• 2012: Jorge Picado and Aleš Pultr: Frames and Locales: Chapter $1$: Spaces and Lattices of Open Sets, $\S 3$ Summing up, Paragraph $3.3$