\begin{section}{Arrow}
The identity operator on $V$ is $\identity{V}$. The composition of
$f$ and $g$ is $\compose{f}{g}$. The inverse of $f$ is
- $\inverse{f}$.
+ $\inverse{f}$. If $f$ is a function and $A$ is a subset of its
+ domain, then the preimage under $f$ of $A$ is $\preimage{f}{A}$.
\end{section}
\begin{section}{Common}
(indexed) union and intersections of things, like
$\unionmany{k=1}{\infty}{A_{k}}$ or
$\intersectmany{k=1}{\infty}{B_{k}}$. The best part about those
- are that they do the right thing in a display equation:
+ is that they do the right thing in a display equation:
%
\begin{equation*}
\unionmany{k=1}{\infty}{A_{k}} = \intersectmany{k=1}{\infty}{B_{k}}
The set of all bounded linear operators from $V$ to $W$ is
$\boundedops[W]{V}$. If $W = V$, then we write $\boundedops{V}$
instead.
+
+ The direct sum of $V$ and $W$ is $\directsum{V}{W}$, of course,
+ but what if $W = V^{\perp}$? Then we wish to indicate that fact by
+ writing $\directsumperp{V}{W}$. That operator should survive a
+ display equation, too, and the weight of the circle should match
+ that of the usual direct sum operator.
+ %
+ \begin{align*}
+ Z = \directsumperp{V}{W}\\
+ \oplus \oplusperp \oplus \oplusperp
+ \end{align*}
+ %
+ Its form should also survive in different font sizes...
+ \Large
+ \begin{align*}
+ Z = \directsumperp{V}{W}\\
+ \oplus \oplusperp \oplus \oplusperp
+ \end{align*}
+ \Huge
+ \begin{align*}
+ Z = \directsumperp{V}{W}\\
+ \oplus \oplusperp \oplus \oplusperp
+ \end{align*}
+ \normalsize
\end{section}
\begin{section}{Listing}
The interior of a set $X$ is $\interior{X}$. Its closure is
$\closure{X}$ and its boundary is $\boundary{X}$.
\end{section}
-
+
\end{document}