Added saturated ideals.

src/topology/main/interiorclosureboundary.tex

@@ -9,6 +9,7 @@
         \item There exists $U \in \fB$ with $U \subset A$.
         \item There exists $U \in \cn(x)$ with $U \subset A$.
     \end{enumerate}
+
     The set of all points satisfying the above is the \textbf{interior} $A^o$ of $A$, which is the largest open set contained in $A$.
 \end{definition}
 \begin{proof}
@@ -28,7 +29,7 @@
         \item For every $B \supset A$ closed, $x \in B$.
         \item For every $U \in \cn(x)$, $U \cap A \ne \emptyset$.
         \item For every $U \in \fB$, $U \cap A \ne \emptyset$.
-        \item There exists a filter $\fF \subset 2^A$ that converges to $\fF$.
+        \item There exists a filter $\fF \subset 2^A$ that converges to $x$.
     \end{enumerate}
 
     The set $\ol{A}$ of all points satisfying the above is the \textbf{closure} of $A$ in $X$. By (1), it is the smallest closed set containing $A$.
@@ -69,6 +70,7 @@
         \item For every $\emptyset \ne U \subset X$ open, $A \cap U \ne \emptyset$.
         \item For every $U \subset X$ open, $\overline{A \cap U} \supset U$.
     \end{enumerate}
+
     If the above holds, then $A$ is a \textbf{dense} subset of $X$.
 \end{definition}
 \begin{proof}