Semilocally contractible => semilocally 0-connected

Author: GeoffreySangston

theorems/T000873.md

@@ -3,7 +3,7 @@ uid: T000873
 if:
   P000239: true
 then:
-  P000229: true
+  P000233: true
 ---
 
-Immediate from the definitions.
+A homotopy restricts to a path.

theorems/T000874.md

@@ -1,9 +1,9 @@
 ---
 uid: T000874
 if:
-  P000224: true
-then:
   P000239: true
+then:
+  P000229: true
 ---
 
 Immediate from the definitions.

theorems/T000875.md

@@ -1,10 +1,9 @@
 ---
 uid: T000875
 if:
-  P000225: true
+  P000224: true
 then:
   P000239: true
 ---
 
-For subsets $V \subset U \subset X$, if $V$
-is contractible in $U$, then it is contractible in $X$.
+Immediate from the definitions.

theorems/T000876.md

@@ -0,0 +1,10 @@
+---
+uid: T000876
+if:
+  P000225: true
+then:
+  P000239: true
+---
+
+For subsets $V \subset U \subset X$, if $V$
+is contractible in $U$, then $V$ is contractible in $X$.