fixes

theorems/T000542.md

@@ -10,6 +10,6 @@ refs:
  name: Generalized paracompactness (Y. Yasui)
 ---
 
-The argument in {{zb:0712.54016}} for this result goes as follows. Suppose $E$ and $F$ are disjoint closed subsets of a shrinking space $X$. Then $\{ X \setminus E , X \setminus F\}$ is an open cover of $X$, so there exists an open cover $\{U, V\}$ of $X$ such that $\overline{U} \subseteq X \setminus E$ and $\overline{V} \subseteq X \setminus F$. Note then that $E \subseteq X \setminus \overilne{U}$, $F \subseteq X \setminus \overline{V}$, and $\left( X \setminus \overline{U} \right) \cap \left( X \setminus \overline{V} \right) = X \setminus \left( \overline{U} \cup \overline{V} \right) = \emptyset$.
+The argument in {{zb:0712.54016}} for this result goes as follows. Suppose $E$ and $F$ are disjoint closed subsets of a shrinking space $X$. Then $\{ X \setminus E , X \setminus F\}$ is an open cover of $X$, so there exists an open cover $\{U, V\}$ of $X$ such that $\overline{U} \subseteq X \setminus E$ and $\overline{V} \subseteq X \setminus F$. Note then that $E \subseteq X \setminus \overline{U}$, $F \subseteq X \setminus \overline{V}$, and $\left( X \setminus \overline{U} \right) \cap \left( X \setminus \overline{V} \right) = X \setminus \left( \overline{U} \cup \overline{V} \right) = \emptyset$.
 
 See also [Dan Ma's Topology Blog post on Spaces with shrinking properties](https://dantopology.wordpress.com/2017/01/05/spaces-with-shrinking-properties/).

theorems/T000543.md

@@ -9,7 +9,7 @@ refs:
  name: Generalized paracompactness (Y. Yasui)
 - zb: "1059.54001"
  name: Encyclopedia of general topology
-- zb: 1052.54001
+- zb: "1052.54001"
  name: General Topology (S. Willard)
 ---