From 6686cfa5d5563732dcf036b3b2335eacf26d210c Mon Sep 17 00:00:00 2001
From: Moniker1998 <adamcz98333@gmail.com>
Date: Thu, 25 Dec 2025 03:58:46 +0100
Subject: [PATCH 1/5] new theorem

---
 theorems/T000806.md | 16 ++++++++++++++++
 1 file changed, 16 insertions(+)
 create mode 100644 theorems/T000806.md

diff --git a/theorems/T000806.md b/theorems/T000806.md
new file mode 100644
index 000000000..f79a6ac26
--- /dev/null
+++ b/theorems/T000806.md
@@ -0,0 +1,16 @@
+---
+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)
+---
+
+Established as corollary 2.2 in {{zb:1126.54010}}. 
+
+In fact, theorem 2.1 shows slightly more generally that if $hL(X) < \mathfrak{t}$ and $X$ is countably compact, then $X$ is sequentially compact. Here $hL(X)$ is the hereditary Lindelof number and $\mathfrak{t}$ is the tower number, where $\omega_1\leq \mathfrak{t}\leq \mathfrak{c}$.

From eae46ba53ff82da1c72c8aee0e45e82026d50992 Mon Sep 17 00:00:00 2001
From: Moniker1998 <adamcz98333@gmail.com>
Date: Fri, 26 Dec 2025 14:30:02 +0100
Subject: [PATCH 2/5] compromising

---
 theorems/T000806.md | 2 --
 1 file changed, 2 deletions(-)

diff --git a/theorems/T000806.md b/theorems/T000806.md
index f79a6ac26..619fcadb5 100644
--- a/theorems/T000806.md
+++ b/theorems/T000806.md
@@ -12,5 +12,3 @@ refs:
 ---
 
 Established as corollary 2.2 in {{zb:1126.54010}}. 
-
-In fact, theorem 2.1 shows slightly more generally that if $hL(X) < \mathfrak{t}$ and $X$ is countably compact, then $X$ is sequentially compact. Here $hL(X)$ is the hereditary Lindelof number and $\mathfrak{t}$ is the tower number, where $\omega_1\leq \mathfrak{t}\leq \mathfrak{c}$.

From 1a02e17f99d9c78acaadf1fb1ea5918d1016a325 Mon Sep 17 00:00:00 2001
From: Moniker1998 <adamcz98333@gmail.com>
Date: Sat, 10 Jan 2026 11:18:40 +0100
Subject: [PATCH 3/5] updated with references and so on

---
 theorems/T000806.md | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/theorems/T000806.md b/theorems/T000806.md
index 619fcadb5..42d3f357a 100644
--- a/theorems/T000806.md
+++ b/theorems/T000806.md
@@ -9,6 +9,8 @@ then:
 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 in {{zb:1126.54010}}. 
+Established as corollary 2.2 of theorem 2.1 in {{zb:1126.54010}}. Note that the proof of theorem 2.1 contains errors which need corrections. These are discussed in {{mo:506776}}.

From 2232cd63af00802ee7987c18757fe530c4c084f0 Mon Sep 17 00:00:00 2001
From: Moniker1998 <88507423+Moniker1998@users.noreply.github.com>
Date: Sat, 10 Jan 2026 22:47:11 +0100
Subject: [PATCH 4/5] Update theorems/T000806.md

Co-authored-by: Patrick Rabau <70125716+prabau@users.noreply.github.com>
---
 theorems/T000806.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/theorems/T000806.md b/theorems/T000806.md
index 42d3f357a..402f6aba0 100644
--- a/theorems/T000806.md
+++ b/theorems/T000806.md
@@ -13,4 +13,4 @@ refs:
     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}}. Note that the proof of theorem 2.1 contains errors which need corrections. These are discussed in {{mo:506776}}.
+Established as Corollary 2.2 of Theorem 2.1 in {{zb:1126.54010}}. Note that the proof of Theorem 2.1 contains errors which need corrections. These are discussed in {{mo:506776}}.

From 5d271212e67c41959dc90a327886796249f7aebb Mon Sep 17 00:00:00 2001
From: Moniker1998 <88507423+Moniker1998@users.noreply.github.com>
Date: Sat, 10 Jan 2026 23:11:08 +0100
Subject: [PATCH 5/5] Update theorems/T000806.md

Co-authored-by: Patrick Rabau <70125716+prabau@users.noreply.github.com>
---
 theorems/T000806.md | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/theorems/T000806.md b/theorems/T000806.md
index 402f6aba0..76d706f00 100644
--- a/theorems/T000806.md
+++ b/theorems/T000806.md
@@ -13,4 +13,6 @@ refs:
     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}}. Note that the proof of Theorem 2.1 contains errors which need corrections. These are discussed in {{mo:506776}}.
+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}}.