T309 is redundant #1596
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T309 is redundant #1596
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Moniker1998
approved these changes
Jan 15, 2026
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T309 (connected +$|X|<\mathfrak c$ => strongly connected)
is redundant as a consequence of
T300 ($|X|<\mathfrak c$ => strongly zero-dimensional) and
T400 (connected + strongly zero-dimensional => strongly connected).
As all three theorems are pretty simple, there is no compelling reason to keep T309.