From 631b88c49d5fb793535102fd37385aeb261d4bf0 Mon Sep 17 00:00:00 2001
From: Patrick Rabau <70125716+prabau@users.noreply.github.com>
Date: Wed, 10 Jun 2026 16:04:33 -0400
Subject: [PATCH] Some trait cleanup for Sphere S169

---
 spaces/S000169/properties/P000016.md | 2 +-
 spaces/S000169/properties/P000086.md | 8 --------
 spaces/S000169/properties/P000137.md | 7 -------
 spaces/S000169/properties/P000199.md | 1 +
 spaces/S000169/properties/P000240.md | 2 +-
 spaces/S000170/properties/P000240.md | 2 +-
 6 files changed, 4 insertions(+), 18 deletions(-)
 delete mode 100644 spaces/S000169/properties/P000086.md
 delete mode 100644 spaces/S000169/properties/P000137.md

diff --git a/spaces/S000169/properties/P000016.md b/spaces/S000169/properties/P000016.md
index 544af86562..16debb1ecb 100644
--- a/spaces/S000169/properties/P000016.md
+++ b/spaces/S000169/properties/P000016.md
@@ -4,4 +4,4 @@ property: P000016
 value: true
 ---
 
-This space is a closed and bounded subspace of the Euclidean space $\mathbb{R}^3$.
\ No newline at end of file
+This space is a closed and bounded subspace of the Euclidean space $\mathbb{R}^3$.
diff --git a/spaces/S000169/properties/P000086.md b/spaces/S000169/properties/P000086.md
deleted file mode 100644
index e176580ce2..0000000000
--- a/spaces/S000169/properties/P000086.md
+++ /dev/null
@@ -1,8 +0,0 @@
----
-space: S000169
-property: P000086
-value: true
----
-
-Any two points on {S169} are related to each other by a rotation of $\mathbb{R}^3$, which restricts to a homeomorphism
-of $S^2$.
diff --git a/spaces/S000169/properties/P000137.md b/spaces/S000169/properties/P000137.md
deleted file mode 100644
index 34d98e8fbc..0000000000
--- a/spaces/S000169/properties/P000137.md
+++ /dev/null
@@ -1,7 +0,0 @@
----
-space: S000169
-property: P000137
-value: false
----
-
-By construction.
diff --git a/spaces/S000169/properties/P000199.md b/spaces/S000169/properties/P000199.md
index a4661ce3b9..9982b77574 100644
--- a/spaces/S000169/properties/P000199.md
+++ b/spaces/S000169/properties/P000199.md
@@ -6,4 +6,5 @@ refs:
 - zb: "1044.55001"
   name: Algebraic Topology (Hatcher)
 ---
+
 This is a consequence of Corollary 2.14 and the statement after Corollary 2.11 of {{zb:1044.55001}}.
diff --git a/spaces/S000169/properties/P000240.md b/spaces/S000169/properties/P000240.md
index 6a944ff6e7..bed4aca6f4 100644
--- a/spaces/S000169/properties/P000240.md
+++ b/spaces/S000169/properties/P000240.md
@@ -14,4 +14,4 @@ The circle can be given a CW complex structure by associating one $0$-cell and o
 
 Equivalently, this follows from the fact that CW complexes are preserved under suspensions, and since the sphere is a suspension of {S170}, which is a CW complex {S170|P240}.
 
-See Example 0.3 in {{zb:1044.55001}}.
\ No newline at end of file
+See Example 0.3 in {{zb:1044.55001}}.
diff --git a/spaces/S000170/properties/P000240.md b/spaces/S000170/properties/P000240.md
index 65ebad2cb0..062b16c773 100644
--- a/spaces/S000170/properties/P000240.md
+++ b/spaces/S000170/properties/P000240.md
@@ -9,4 +9,4 @@ refs:
 
 The circle can be given a CW complex structure by associating one $0$-cell and one $1$-cell: Start with $X_0=\{*\}$, then attach a $1$-cell $D^1 = [-1,1]$ by identifying both boundary points with the $0$-cell (define $f_1: \partial D^1 \to X_0$ by $f_1(\pm 1) = *$.)
 
-See Example 0.3 in {{zb:1044.55001}}.
\ No newline at end of file
+See Example 0.3 in {{zb:1044.55001}}.