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spaces/S000209/README.md

@@ -1,10 +1,13 @@
 ---
 uid: S000209
 name: Circle with two origins
+refs:
+  - wikipedia: Alexandroff_extension
+    name: Alexandroff extension on Wikipedia
 ---
 
 Choose a point $0 \in S^1$ to be called the origin, and replace $0$ with two origins $0_1$ and $0_2$. Basic open neighborhoods of a point $x \neq 0$ are Euclidean open neighborhoods of $x$ not containing $0$. Basic open neighborhoods of each origin $0_i$ are of the form $(U\setminus\{0\})\cup\{0_i\}$ with $U$ a Euclidean open neighborhood of $0$.
 
-Let $\{1, 2\}$ have the discrete topology. $X$ is homeomorphic to the quotient space of $S^1 \times \{1, 2\}$ obtained by identifying $\langle \theta, 1 \rangle$ and $\langle \theta, 2 \rangle$ exactly when $\theta \not\equiv 0 \mod 2\pi$.
+Let $\{1, 2\}$ have the discrete topology. $X$ is homeomorphic to the quotient space of $S^1 \times \{1, 2\}$ obtained by identifying $\langle \theta, 1 \rangle$ and $\langle \theta, 2 \rangle$ exactly when $\theta {\not\equiv} 0 \mod 2\pi$.
 
-$X$ is homeomorphic to the one-point compactification of {S83}.
+$X$ is homeomorphic to the Alexandroff extension of {S83}.

spaces/S000209/properties/P000016.md

@@ -2,6 +2,9 @@
 space: S000209
 property: P000016
 value: true
+refs:
+  - wikipedia: Alexandroff_extension
+    name: Alexandroff extension on Wikipedia
 ---
 
-$X$ is homeomorphic to the one-point compactification of {S83}.
+$X$ is homeomorphic to the Alexandroff extension of {S83}.