pi-base · prabau · Apr 19, 2026 · Apr 18, 2026 · Apr 18, 2026 · Apr 19, 2026
diff --git a/spaces/S000025/properties/P000087.md b/spaces/S000025/properties/P000087.md
diff --git a/spaces/S000025/properties/P000238.md b/spaces/S000025/properties/P000238.md
@@ -0,0 +1,7 @@
+---
+space: S000025
+property: P000238
+value: true
+---
+
+The standard addition and scalar multiplication on $\mathbb R$ are continuous, and together satisfy the axioms of a real vector space.
diff --git a/spaces/S000030/properties/P000087.md b/spaces/S000030/properties/P000087.md
diff --git a/spaces/S000030/properties/P000199.md b/spaces/S000030/properties/P000199.md
diff --git a/spaces/S000030/properties/P000238.md b/spaces/S000030/properties/P000238.md
@@ -0,0 +1,7 @@
+---
+space: S000030
+property: P000238
+value: true
+---
+
+$\mathbb{R}^\omega$ is a product of topological vector spaces, namely $\mathbb{R}$. And {S25|P238}.
diff --git a/spaces/S000176/properties/P000087.md b/spaces/S000176/properties/P000087.md
diff --git a/spaces/S000176/properties/P000199.md b/spaces/S000176/properties/P000199.md
diff --git a/spaces/S000176/properties/P000238.md b/spaces/S000176/properties/P000238.md
@@ -0,0 +1,7 @@
+---
+space: S000176
+property: P000238
+value: true
+---
+
+The standard addition and scalar multiplication on $\mathbb R^2$ are continuous, and together satisfy the axioms of a real vector space.