Add references. Apply fixes.

Author: GeoffreySangston

properties/P000087.md

@@ -8,10 +8,10 @@ refs:
     name: Topology (Munkres)
 ---
 
-There exists a continuous group operation $(x,y)\mapsto x\cdot y$ on the space such that
-the inverse operation $x\mapsto x^{-1}$ is also continuous.
+$X$ is homeomorphic to a topological group.
 
-Equivalently, $X$ is homeomorphic to a topological group.
+Equivalently, there exists a continuous group operation $(x,y)\mapsto x\cdot y$ on the space such that
+the inverse operation $x\mapsto x^{-1}$ is also continuous.
 
 Contrary to Munkres or Willard, we do not assume any separation axiom like {P3}, {P2} or {P1}.
 

properties/P000238.md

@@ -2,9 +2,23 @@
 uid: P000238
 name: Has a real TVS topology
 aliases:
-- Topological vector space, TVS
+  - Topological vector space
+  - TVS
+refs:
+  - wikipedia: Topological_vector_space
+    name: Topological vector space on Wikipedia
+  - zb: "0867.46001"
+    name: Functional analysis. 2nd ed. (W. Rudin)
 ---
 
-There exists a continuous commutative group operation $(x, y) \mapsto x + y$ on the space such that the inverse operation $x \mapsto -x$ is also continuous. And there exists a continuous scalar multiplication operation $\mathbb{R} \times X \to X$, $(\lambda, x) \mapsto \lambda x$, where $\mathbb{R}$ has the Euclidean topology, such that these operations together satisfy the axioms of a real vector space.
+$X$ is homeomorphic to a real topological vector space (TVS).
 
-Equivalently, $X$ is homeomorphic to a real topological vector space (TVS).
+Equivalently, there exists a continuous commutative group operation $(x, y) \mapsto x + y$, and a continuous scalar multiplication operation $\mathbb{R} \times X \to X$, $(\lambda, x) \mapsto \lambda x$, where $\mathbb{R}$ has the Euclidean topology, such that these operations together satisfy the axioms of a real vector space.
+
+Many authors, such as Rudin, additionally require separation axioms like {P3}, {P2} or {P1}, though we do not.
+
+----
+#### Meta-properties
+
+- This property is preserved by arbitrary products.
+- This property is preserved by $\Sigma$-products.