From e37bdd4e3fab3d3ccaa2c4ce2534e48fff0533e9 Mon Sep 17 00:00:00 2001
From: Moniker1998 <88507423+Moniker1998@users.noreply.github.com>
Date: Tue, 28 Jan 2025 22:14:18 +0100
Subject: [PATCH] T698: WLC + para-Lindelof + connected => Lindelof (#1215)

---
 theorems/T000698.md | 17 +++++++++++++++++
 1 file changed, 17 insertions(+)
 create mode 100644 theorems/T000698.md

diff --git a/theorems/T000698.md b/theorems/T000698.md
new file mode 100644
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+++ b/theorems/T000698.md
@@ -0,0 +1,17 @@
+---
+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.