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feat: prove T597, hyperconnected with an isolated point gives a generic point - #1334

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kisonecat:formalize-T597
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kisonecat wants to merge 1 commit into
felixpernegger:masterfrom
kisonecat:formalize-T597

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Adds T597: a hyperconnected space with an isolated point has a generic point.

If p is isolated then {p} is a nonempty open set, so hyperconnectedness makes every
nonempty open set meet {p} — that is, contain p. Hence every neighbourhood of every point
meets {p}, so closure {p} is the whole space and p is generic.

Closes #1028.

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T597: Hyperconnected (P39) + Has an isolated point (P139) => Has a generic point (P201)

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