fern needs to proofread properly

Author: fernwarwick

blog_posts/redefining-continuity.html

@@ -58,9 +58,7 @@ <h2>
   </p>
   <p>
    <strong>
-    In topology, limits are not unique
-   </strong>
-   . Some topological spaces have sequences that do not converge, some converge on one point, some converge on more than one point and some converge on the entire domain. A clear cut solution for continuity cannot rely on a limit-based definition.
+    In topology, limits are not unique</strong>. Some topological spaces have sequences that do not converge, some converge on one point, some converge on more than one point and some converge on the entire domain. A clear cut solution for continuity cannot rely on a limit-based definition.
   </p>
   <p>
    <strong>
@@ -69,7 +67,7 @@ <h2>
    This is a problem, since the aim of topology is to find invariant properties under continuity.
   </p>
   <p>
-   It is clear that this definition does not suffice for our purposes. But how do we find such a definition?
+   It is clear that this definition does not suffice for our purposes. But how do we find a better one?
   </p>
   <h2>
    Introducing: the open ball
@@ -201,7 +199,7 @@ <h2>
    <em>
     local
    </em>
-   when describing the map. This is because while the inverse of $\sin$ maps to $[-\pi,\pi]$, the preimage extends out infinitely:[^5]
+   when describing the map. This is because while the inverse of $\sin$ maps to $[-\pi,\pi]$, the preimage extends out infinitely:
   </p>
   <p>
    <img alt="Missed values" src="sin-missed-values.jpg"/>