diff --git a/spaces/S000174/properties/P000023.md b/spaces/S000174/properties/P000023.md
new file mode 100644
index 0000000000..1154b6372e
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+++ b/spaces/S000174/properties/P000023.md
@@ -0,0 +1,11 @@
+---
+space: S000174
+property: P000023
+value: false
+---
+
+At the point $p=(\omega, \omega, \dots)$, the clopen sets
+$\{\omega\}^n \times (\omega+1)^\omega$ form a neighborhood base. Each of
+these sets has a topology finer than the product topology on
+$\{\omega\}^n \times (\omega+1)^\omega$ when $\omega+1$ is discrete. The
+latter space is not compact, so none of these neighborhoods is compact.
diff --git a/spaces/S000174/properties/P000051.md b/spaces/S000174/properties/P000051.md
new file mode 100644
index 0000000000..25f7a2e0c0
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+++ b/spaces/S000174/properties/P000051.md
@@ -0,0 +1,7 @@
+---
+space: S000174
+property: P000051
+value: false
+---
+
+The subspace $2 ^ \omega \setminus \{(0,0,\dots)\} \subseteq X$ is homeomorphic to Cantor set without a point, and so has no isolated points.
diff --git a/spaces/S000174/properties/P000062.md b/spaces/S000174/properties/P000062.md
new file mode 100644
index 0000000000..672208b51a
--- /dev/null
+++ b/spaces/S000174/properties/P000062.md
@@ -0,0 +1,10 @@
+---
+space: S000174
+property: P000062
+value: false
+---
+
+The collection $\{\xi^\omega : \xi < \omega_1\}$ is an open cover of $X$.
+Every countable subcollection has union contained in $\xi^\omega$ for some
+$\xi < \omega_1$, and $\xi^\omega$ is a proper closed subset of $X$. Thus,
+no countable subcollection has dense union.
diff --git a/spaces/S000174/properties/P000065.md b/spaces/S000174/properties/P000065.md
new file mode 100644
index 0000000000..69fecf56c4
--- /dev/null
+++ b/spaces/S000174/properties/P000065.md
@@ -0,0 +1,9 @@
+---
+space: S000174
+property: P000065
+value: true
+---
+
+
+\[\mathfrak c = |2^\omega| \leq |\omega_1^\omega|
+\leq |(2^\omega)^\omega| = \mathfrak c\]
diff --git a/spaces/S000174/properties/P000083.md b/spaces/S000174/properties/P000083.md
new file mode 100644
index 0000000000..6be284efd6
--- /dev/null
+++ b/spaces/S000174/properties/P000083.md
@@ -0,0 +1,16 @@
+---
+space: S000174
+property: P000083
+value: false
+refs:
+  - doi: 10.4064/FM-97-2-53-55
+    name: "A perfectly normal locally metrizable non-paracompact space"
+  - zb: "0593.28016"
+    name: Borel measures (Gardner and Pfeffer)
+---
+
+Proposition 2 of {{doi:10.4064/FM-97-2-53-55}} constructs a locally countable
+subspace of $X$ which is not $\sigma$-discrete. By Theorem 13.3 of
+{{zb:0593.28016}}, every locally countable subspace of
+a weakly $\delta\theta$-refinable space is $\sigma$-discrete. Hence $X$ is not
+weakly $\delta\theta$-refinable and, in particular, is not meta-Lindelöf.
diff --git a/spaces/S000174/properties/P000093.md b/spaces/S000174/properties/P000093.md
new file mode 100644
index 0000000000..7b68071754
--- /dev/null
+++ b/spaces/S000174/properties/P000093.md
@@ -0,0 +1,7 @@
+---
+space: S000174
+property: P000093
+value: false
+---
+
+The point $(\omega, \omega,\dots) \in X$ has no countable neighborhood.
diff --git a/spaces/S000174/properties/P000139.md b/spaces/S000174/properties/P000139.md
new file mode 100644
index 0000000000..69d03db20e
--- /dev/null
+++ b/spaces/S000174/properties/P000139.md
@@ -0,0 +1,7 @@
+---
+space: S000174
+property: P000139
+value: true
+---
+
+The point $p := (0, 0, \dots) \in X$ is isolated since $\{p\} = 1^\omega$ where $1 = \{0\}$.
diff --git a/spaces/S000174/properties/P000163.md b/spaces/S000174/properties/P000163.md
deleted file mode 100644
index 03beb65bf6..0000000000
--- a/spaces/S000174/properties/P000163.md
+++ /dev/null
@@ -1,7 +0,0 @@
----
-space: S000174
-property: P000163
-value: true
----
-
-$|X| = |\omega_1^\omega| \leq (2^\omega)^\omega = 2^\omega = \mathfrak{c}$.
diff --git a/spaces/S000174/properties/P000194.md b/spaces/S000174/properties/P000194.md
new file mode 100644
index 0000000000..7a3456cb91
--- /dev/null
+++ b/spaces/S000174/properties/P000194.md
@@ -0,0 +1,16 @@
+---
+space: S000174
+property: P000194
+value: false
+refs:
+  - doi: 10.4064/FM-97-2-53-55
+    name: "A perfectly normal locally metrizable non-paracompact space"
+  - zb: "0593.28016"
+    name: Borel measures (Gardner and Pfeffer)
+---
+
+Proposition 2 of {{doi:10.4064/FM-97-2-53-55}} constructs a locally countable
+subspace of $X$ which is not $\sigma$-discrete. By Theorem 13.3 of
+{{zb:0593.28016}}, every locally countable subspace of
+a weakly $\delta\theta$-refinable space is $\sigma$-discrete. Hence $X$ is not
+weakly $\delta\theta$-refinable and, in particular, is not submetacompact.