inputs/lecture_03.tex

@@ -165,13 +165,7 @@
         Since the cantor space embeds into $X$,
         we get the lower bound.
         Since $X$ is second countable and Hausdorff,
-        we get the upper bound:
-        Let $\langle U_n : n < \omega \rangle$ be a countable basis.
-        Consider the injective function
-        \begin{IEEEeqnarray*}{rCl}
-            f\colon X &\longrightarrow & 2^{ \omega} \\
-             x &\longmapsto & \{n : x \in U_n\}.
-        \end{IEEEeqnarray*}
+        we get the upper bound.%
     }{Lower bound:  $2^{\N} \hookrightarrow X$,
         upper bound: \nth{2} countable and Hausdorff.}
 \end{proof}