Update theorems/T000847.md

Co-authored-by: Patrick Rabau <70125716+prabau@users.noreply.github.com>

Author: GeoffreySangston

theorems/T000847.md

@@ -6,6 +6,5 @@ then:
   P000223: true
 ---
 
-A locally Euclidean space admits a basis of Euclidean open balls. A Euclidean open ball is homeomorphic to
-$\mathbb{R}^n$. Then the claim follows because the map $\mathbb{R}^n \times [0, 1] \to \mathbb{R}^n$,
-$(p, t) \mapsto (1-t)p$, is a homotopy from the identity map of Euclidean space to a constant map.
+For each $x\in X$, every neighborhood of $x$ contains an open neighborhood homeomorphic to some Euclidean space $\mathbb R^n$.
+And $\mathbb R^n$ is {P199} as it can be deformation retracted to a point using a straight-line homotopy.