Give up on Topologies Ass 3

Author: DoctorDalek1963

second-year/MA260-Norms-Metrics-and-Topologies/Ass-3/Dyson_Dyson_5503449_MA260_Assignment_3.pdf

@@ -67,41 +67,40 @@
 
 $A = \{(x, 0) : x \in \R\}$. Since this a straight line in $\R^2$, $\partial A = A$ and $A^\circ = \emptyset$.
 
-% TODO: Justify and nice-ify
-$B = \{(x, y) : x, y \in \R, x > y, y \ne 0\} = \{(x, y) : x, y \in \R, x > y\} \setminus A$.
+% TODO: Justify
+$B = \{(x, y) : x, y \in \R, x > y, y \ne 0\} = \{(x, y) : x, y \in \R, x > y\} \setminus A$. Therefore \[
+\partial B = \{(x, x) : x \in \R\} \cup \{(x, 0) : x \in \R, x > 0\}
+\] and $B^\circ = B$.
 
-$\partial B = \{(x, x) : x \in \R\} \cup \{(x, 0) : x \in \R, x > 0\}$.
-
-$B^\circ = B$.
-
-$C = \{(x, y) : x, y \in \R, x > y\} \cup A$.
-
-$\partial C = \{(x, x) : x \in \R\} \cup \{(x, 0) : x \in \R, x < 0\}$.
-
-$C^\circ = \{(x, y) : x, y \in \R, x > y\}$.
+$C = \{(x, y) : x, y \in \R, x > y\} \cup A$. Therefore \[
+\partial C = \{(x, x) : x \in \R\} \cup \{(x, 0) : x \in \R, x < 0\}
+\] and \[
+C^\circ = \{(x, y) : x, y \in \R, x > y\}.
+\]
 
 % }}}
 
 % {{{ Q4
-\newquestion{4}
+% \newquestion{4}
 
-\begin{questionbody}
-Show that $X$ is Hausdorff if and only if the \textit{diagonal} $\Delta = \{x \times x : x \in X\}$ is closed in $X \times X$.
-\end{questionbody}
+% \begin{questionbody}
+% Show that $X$ is Hausdorff if and only if the \textit{diagonal} $\Delta = \{x \times x : x \in X\}$ is closed in $X \times X$.
+% \end{questionbody}
+
+% Answer
 
-Answer
 % }}}
 
 % {{{ Q5
-\newquestion{5}
+% \newquestion{5}
 
-\begin{questionbody}
-Let $A \subset X$ and let $f : A \to Y$ be continuous. Suppose $Y$ is Hausdorff. Show that there is at most one continuous function $g : \ol A \to Y$ such that $g(x) = f(x)$ for all $x \in A$.
-\end{questionbody}
+% \begin{questionbody}
+% Let $A \subset X$ and let $f : A \to Y$ be continuous. Suppose $Y$ is Hausdorff. Show that there is at most one continuous function $g : \ol A \to Y$ such that $g(x) = f(x)$ for all $x \in A$.
+% \end{questionbody}
 
-% See problem sheet 5, exercise 5
+% % See problem sheet 5, exercise 5
 
-Answer
+% Answer
 
 % }}}