From 27e4bc7f27e226e9c69858a54484f8fde84fceda Mon Sep 17 00:00:00 2001
From: Batixx <s59fpern@uni-bonn.de>
Date: Sat, 17 Jan 2026 21:23:00 +0100
Subject: [PATCH] traits

---
 spaces/S000139/properties/P000064.md | 10 ----------
 spaces/S000139/properties/P000206.md |  8 ++++++++
 spaces/S000139/properties/P000214.md |  7 +++++++
 3 files changed, 15 insertions(+), 10 deletions(-)
 delete mode 100644 spaces/S000139/properties/P000064.md
 create mode 100644 spaces/S000139/properties/P000206.md
 create mode 100644 spaces/S000139/properties/P000214.md

diff --git a/spaces/S000139/properties/P000064.md b/spaces/S000139/properties/P000064.md
deleted file mode 100644
index 4c6745586f..0000000000
--- a/spaces/S000139/properties/P000064.md
+++ /dev/null
@@ -1,10 +0,0 @@
----
-space: S000139
-property: P000064
-value: true
-refs:
-  - wikipedia: Baire_space
-    name: Baire space on Wikipedia
----
-
-The subspace $X\setminus\{\infty\}$ is Baire (because it is locally compact and Hausdorff) and dense in $X.$
diff --git a/spaces/S000139/properties/P000206.md b/spaces/S000139/properties/P000206.md
new file mode 100644
index 0000000000..fadb971900
--- /dev/null
+++ b/spaces/S000139/properties/P000206.md
@@ -0,0 +1,8 @@
+---
+space: S000139
+property: P000206
+value: true
+---
+
+If Player I picks $x_n= \infty$ in every turn, clearly $\infty \in \bigcap \{U_n:n<\omega\}$.
+So suppose for some $n$, $x_n\neq \infty$, then Player II can choose $V_n$ to be homeomorphic to {S25} and the assertion follows since {S25|P206}.
diff --git a/spaces/S000139/properties/P000214.md b/spaces/S000139/properties/P000214.md
new file mode 100644
index 0000000000..597d11ae34
--- /dev/null
+++ b/spaces/S000139/properties/P000214.md
@@ -0,0 +1,7 @@
+---
+space: S000139
+property: P000214
+value: false
+---
+
+For $m \in \mathbb{N}$, let $S_m := \{m + \frac{1}{2}, m + \frac{1}{3}, \dots\}$. Clearly $S_m$ converges to $\infty$, but picking any countable infinite $S$ with $S \cap S_m \neq \emptyset$ for infinitely many $m$ does not.