From ea673f3c323f47aadd16684b6f495755df6950a6 Mon Sep 17 00:00:00 2001
From: Patrick Rabau <70125716+prabau@users.noreply.github.com>
Date: Mon, 7 Oct 2024 15:24:48 -0400
Subject: [PATCH] fixes

---
 spaces/S000038/properties/P000086.md | 2 +-
 spaces/S000044/properties/P000086.md | 3 +--
 spaces/S000045/properties/P000086.md | 2 +-
 3 files changed, 3 insertions(+), 4 deletions(-)

diff --git a/spaces/S000038/properties/P000086.md b/spaces/S000038/properties/P000086.md
index 9be2abfda..60c8d7168 100644
--- a/spaces/S000038/properties/P000086.md
+++ b/spaces/S000038/properties/P000086.md
@@ -4,4 +4,4 @@ property: P000086
 value: false
 ---
 
-Follows as every point except $\langle 0,0 \rangle$ is a cut point.
+Every point except $\langle 0,0 \rangle$ is a cut point, and $\langle 0,0 \rangle$ is not.
diff --git a/spaces/S000044/properties/P000086.md b/spaces/S000044/properties/P000086.md
index 4ff6a03ed..c3bd22cee 100644
--- a/spaces/S000044/properties/P000086.md
+++ b/spaces/S000044/properties/P000086.md
@@ -4,5 +4,4 @@ property: P000086
 value: false
 ---
 
-$1/3$ belongs to a single open set $(0,1)$, but
-$2/5$ belongs to two open sets $(0,1)$ and $(0,1/2)$.
+$1$ is a closed point, but $1/3$ is not.
diff --git a/spaces/S000045/properties/P000086.md b/spaces/S000045/properties/P000086.md
index 48ece6cc5..5f5fde3de 100644
--- a/spaces/S000045/properties/P000086.md
+++ b/spaces/S000045/properties/P000086.md
@@ -4,4 +4,4 @@ property: P000086
 value: false
 ---
 
-$0$ belongs to every open set, but $1$ does not.
+$0$ belongs to every nonempty open set, but $1$ does not.