From b32934749bc12c5b35d2898625cb246f07d5b685 Mon Sep 17 00:00:00 2001
From: danflapjax <12000932+danflapjax@users.noreply.github.com>
Date: Wed, 16 Oct 2024 13:39:07 -0700
Subject: [PATCH] Update T000550.md

---
 theorems/T000550.md | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/theorems/T000550.md b/theorems/T000550.md
index 5ae939464..3ab1ae577 100644
--- a/theorems/T000550.md
+++ b/theorems/T000550.md
@@ -8,4 +8,5 @@ then:
   P000146: true
 ---
 
-In a {P39} space $X$, every nonempty open set is dense, so to admit a shrinking, every open cover must contain $X$. Thus, any open cover admits a clopen refinement.
+In a {P39} space $X$, the closure of every nonempty open set is $X$, so any open cover that admits a shrinking must contain $X$ (as otherwise each of its open sets could only contain the closure of $\varnothing$).
+Thus, any such open cover admits an open refinement to the partition $\{X\}$.