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Countably compact hereditarily Lindelof spaces are sequentially compact #1551

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prabau merged 5 commits into from
Jan 10, 2026
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Countably compact hereditarily Lindelof spaces are sequentially compact #1551

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6686cfa
new theorem
Moniker1998 Dec 25, 2025
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compromising
Moniker1998 Dec 26, 2025
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updated with references and so on
Moniker1998 Jan 10, 2026
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Update theorems/T000806.md
Moniker1998 Jan 10, 2026
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Update theorems/T000806.md
Moniker1998 Jan 10, 2026
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18 changes: 18 additions & 0 deletions theorems/T000806.md
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---
uid: T000806
if:
and:
- P000019: true
- P000131: true
then:
P000020: true
refs:
- zb: "1126.54010"
name: When is a compact space sequentially compact? (O. Alas, R. Wilson)
- mo: 506776
name: Proof of Alas and Wilson that countably compact hereditarily Lindelof spaces are sequentially compact
---

Established as Corollary 2.2 of Theorem 2.1 in {{zb:1126.54010}}
(available [here](https://topology.nipissingu.ca/tp/reprints/v29/tp29201.pdf)).
Note that the proof of Theorem 2.1 contains errors which need corrections. These are discussed in {{mo:506776}}.