From 463478fe2d7da7266a15a87ce5db568361ad0978 Mon Sep 17 00:00:00 2001
From: Patrick Rabau <70125716+prabau@users.noreply.github.com>
Date: Thu, 13 Aug 2026 02:12:04 -0400
Subject: [PATCH 1/2] More traits for S125 Knaster-Kuratowski fan

---
 spaces/S000125/README.md             |  9 ++++++---
 spaces/S000125/properties/P000022.md | 11 -----------
 spaces/S000125/properties/P000023.md | 11 -----------
 spaces/S000125/properties/P000041.md |  7 ++-----
 spaces/S000125/properties/P000055.md |  9 +++++++++
 5 files changed, 17 insertions(+), 30 deletions(-)
 delete mode 100644 spaces/S000125/properties/P000022.md
 delete mode 100644 spaces/S000125/properties/P000023.md
 create mode 100644 spaces/S000125/properties/P000055.md

diff --git a/spaces/S000125/README.md b/spaces/S000125/README.md
index 50a52980d6..582d298313 100644
--- a/spaces/S000125/README.md
+++ b/spaces/S000125/README.md
@@ -10,11 +10,14 @@ refs:
 - wikipedia: Knaster-Kuratowski_fan
   name: Knaster-Kuratowski fan
 ---
-For any $a \in [0,1]$, let $L(a)$ be the line segment from $(a,0)$ to $p = (\frac{1}{2}, \frac{1}{2})$. Let $\mathcal{C}$ be the middle-thirds Cantor set in the unit interval, $\mathcal{E}$ the endpoints of the removed intervals and $\mathcal{F} = \mathcal{C} \setminus \mathcal{E}$. Define $A = \{(x,y) \in L(c)\ |\ c \in \mathcal{E}, y \in \mathbb{Q}\}$ and $B = \{(x,y) \in L(c)\ |\ c \in \mathcal{F}, y \not\in \mathbb{Q}\}$. This space is $X = A \cup B \subset \mathbb{R}^2$ with the subspace topology.
+
+$X$ is a subspace of {S176} defined as follows.
+For any $a \in [0,1]$, let $L(a)$ be the closed line segment from $(a,0)$ to $p = (\frac{1}{2}, \frac{1}{2})$.
+Let $C$ be the middle-thirds Cantor set in the unit interval, $E$ the set of endpoints of the removed intervals and $F = C\setminus E$.
+Define $A = \{(x,y) \in L(c):c \in E, y \in \mathbb Q\}$ and $B = \{(x,y) \in L(c):c \in F, y \not\in \mathbb Q\}$.
+Then take $X = A \cup B\subseteq\mathbb R^2$ with the subspace topology.
 
 The subspace $X\setminus\{p\}$ obtained by removing the apex point is {S126}.
 
 Defined as counterexample #128 ("Cantor's Leaky Tent")
 in {{zb:0386.54001}}.
-
-<!-- ![](http://i.imgur.com/P36Jx0z.png?1) -->
diff --git a/spaces/S000125/properties/P000022.md b/spaces/S000125/properties/P000022.md
deleted file mode 100644
index ebb2ee4948..0000000000
--- a/spaces/S000125/properties/P000022.md
+++ /dev/null
@@ -1,11 +0,0 @@
----
-space: S000125
-property: P000022
-value: false
-refs:
-- zb: "0386.54001"
-  name: Counterexamples in Topology
----
-
-Asserted in the General Reference Chart for space #128 in
-{{zb:0386.54001}}.
diff --git a/spaces/S000125/properties/P000023.md b/spaces/S000125/properties/P000023.md
deleted file mode 100644
index e74a0a564b..0000000000
--- a/spaces/S000125/properties/P000023.md
+++ /dev/null
@@ -1,11 +0,0 @@
----
-space: S000125
-property: P000023
-value: false
-refs:
-- zb: "0386.54001"
-  name: Counterexamples in Topology
----
-
-Asserted in the General Reference Chart for space #128 in
-{{zb:0386.54001}}.
diff --git a/spaces/S000125/properties/P000041.md b/spaces/S000125/properties/P000041.md
index 7818e1d031..6125857d9b 100644
--- a/spaces/S000125/properties/P000041.md
+++ b/spaces/S000125/properties/P000041.md
@@ -2,10 +2,7 @@
 space: S000125
 property: P000041
 value: false
-refs:
-- zb: "0386.54001"
-  name: Counterexamples in Topology
 ---
 
-Asserted in the General Reference Chart for space #128 in
-{{zb:0386.54001}}.
+{S126} is an open subset of $X$,
+and {S126|P41}.
diff --git a/spaces/S000125/properties/P000055.md b/spaces/S000125/properties/P000055.md
new file mode 100644
index 0000000000..5206b2b684
--- /dev/null
+++ b/spaces/S000125/properties/P000055.md
@@ -0,0 +1,9 @@
+---
+space: S000125
+property: P000055
+value: false
+---
+
+For any $c\in E$ the closed set $L(c)\cap X\subseteq X$ is homeomorphic to $[0,1/2]\cap\mathbb Q$,
+which in turn contains a closed set homeomorphic to {S27}.
+And {S27|P55}.

From a1924ae7f0df5a15fe8236e5f77c1f68977fe144 Mon Sep 17 00:00:00 2001
From: Patrick Rabau <70125716+prabau@users.noreply.github.com>
Date: Wed, 19 Aug 2026 00:02:58 -0400
Subject: [PATCH 2/2] not Menger

---
 spaces/S000125/properties/P000055.md | 4 ++--
 spaces/S000125/properties/P000066.md | 9 +++++++++
 2 files changed, 11 insertions(+), 2 deletions(-)
 create mode 100644 spaces/S000125/properties/P000066.md

diff --git a/spaces/S000125/properties/P000055.md b/spaces/S000125/properties/P000055.md
index 5206b2b684..97ff45df6c 100644
--- a/spaces/S000125/properties/P000055.md
+++ b/spaces/S000125/properties/P000055.md
@@ -4,6 +4,6 @@ property: P000055
 value: false
 ---
 
-For any $c\in E$ the closed set $L(c)\cap X\subseteq X$ is homeomorphic to $[0,1/2]\cap\mathbb Q$,
-which in turn contains a closed set homeomorphic to {S27}.
+Take some $c\in E$.
+The closed set $L(c)\cap X\subseteq X$ contains a closed set homeomorphic to {S27}.
 And {S27|P55}.
diff --git a/spaces/S000125/properties/P000066.md b/spaces/S000125/properties/P000066.md
new file mode 100644
index 0000000000..c390447f19
--- /dev/null
+++ b/spaces/S000125/properties/P000066.md
@@ -0,0 +1,9 @@
+---
+space: S000125
+property: P000066
+value: false
+---
+
+Take some $c\in F$.
+The closed set $L(c)\cap X\subseteq X$ contains a closed set homeomorphic to {S28}.
+And {S28|P66}.