Definitions

Author: GeoffreySangston

properties/P000087.md

@@ -11,6 +11,8 @@ refs:
 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.
 
+Equivalently, $X$ is homeomorphic to a topological group.
+
 Contrary to Munkres or Willard, we do not assume any separation axiom like {P3}, {P2} or {P1}.
 
 ----

properties/P000238.md

@@ -0,0 +1,10 @@
+---
+uid: P000238
+name: Has a real TVS topology
+aliases:
+- Topological vector space, TVS
+---
+
+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.
+
+Equivalently, $X$ is homeomorphic to a real topological vector space (TVS).