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T553 update: hereditarily connected => locally contractible #1729

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Merged
felixpernegger merged 2 commits into from
Apr 12, 2026
Merged

T553 update: hereditarily connected => locally contractible #1729

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e1292ea
T553 update: hereditarily connected => locally contractible
prabau Apr 10, 2026
2e57cdd
Remove redundant T316
prabau Apr 11, 2026
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9 changes: 0 additions & 9 deletions spaces/S000221/properties/P000230.md
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12 changes: 0 additions & 12 deletions theorems/T000316.md
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5 changes: 3 additions & 2 deletions theorems/T000553.md
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Original file line number Diff line number Diff line change
Expand Up @@ -3,7 +3,8 @@ uid: T000553
if:
P000196: true
then:
P000042: true
P000223: true
---

Every subset of a {P196} space is {P40}, and {T38}.
Since {T585}, every nonempty subset of $X$ is also {P199}.
In particular, every open neighborhood of every point is {P199}.
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