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paracompact + locally compact + connected implies exhaustible by compacts #1215

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Jan 28, 2025
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paracompact + locally compact + connected implies exhaustible by compacts #1215

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paracompact + locally compact + connected implies sigma-compact
Moniker1998 Jan 26, 2025
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updated to make it stronger
Moniker1998 Jan 27, 2025
fe867e4
Update theorems/T000698.md
Moniker1998 Jan 28, 2025
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17 changes: 17 additions & 0 deletions theorems/T000698.md
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---
uid: T000698
if:
and:
- P000023: true
- P000105: true
- P000036: true
then:
P000018: true
refs:
- mathse: 5028016
name: Answer to "Connected, locally compact, paracompact Hausdorff space is exhaustible by compacts"
---

Call a space *weakly locally Lindelöf* if every point has a neighborhood that is Lindelöf.

In {{mathse:5028016}} it is shown that a {P36} weakly locally Lindelöf {P105} space is {P18}, and {P23} implies weakly locally Lindelöf.