Defining a functional map

Question

I am trying to define in latex the following function:

We also want everything to be aligned.

I tried including another align environment but it seems this is not possible:

\begin{align*} 
\Psi: C([0,1],\mathbb{R}) &\longrightarrow C([0,1],\mathbb{R}) \\ 
f & \longmapsto \Psi f:\begin{align*}
[0,1]&\longrightarrow \mathbb{R}\\
x &\longmapsto (\Psi(f))(x)=\int_0^x\!f(y)\,\mathrm{d}y
\end{align*}
\end{align*}

How to fix this problem?

Answer 1

Use aligned inside align*:

\documentclass{article}
\usepackage{amsmath}
\usepackage{amssymb}
\begin{document}

\begin{align*} 
  \Psi: C([0,1],\mathbb{R}) &\longrightarrow C([0,1],\mathbb{R}) \\ 
  f & \longmapsto \Psi(f):
  \begin{aligned}[t]
    [0,1] & \longrightarrow \mathbb{R} \\
    x     & \longmapsto (\Psi(f))(x)=\int_0^x\!f(y)\,\mathrm{d}y
  \end{aligned}
\end{align*}

\end{document}

Similar Question: Problem with multiple alignments in equation

Answer 2

Using alignat enviroment and text and math font Cambria with XeLaTeX engine.

\documentclass[12pt]{article}
\usepackage{fontspec,unicode-math}
\setmainfont{Cambria}
\setmathfont{Cambria Math}

\begin{document}
Text
\begin{alignat*}{2}
&\Psi \colon C([0,1],\mathbb{R}) \longrightarrow C([0,1],\mathbb{R}) \\
& f \longmapsto \Psi(f)\colon [0,1] \longrightarrow \mathbb{R} \\
& x \longmapsto (\Psi(f))(x) = \int_0^x\!f(y)\,\mathrm{d}y
\end{alignat*}

\end{document}

Another option can be this:

\documentclass[12pt]{article}
\usepackage{fontspec,unicode-math}
\setmainfont{Cambria}
\setmathfont{Cambria Math}

\begin{document}
Textual mode 
\begin{alignat*}{2}
\Psi \colon C([0,1],\mathbb{R}) &\longrightarrow C([0,1],\mathbb{R}) \\
 f& \longmapsto \Psi(f)\colon [0,1] \longrightarrow \mathbb{R} \\
 x& \longmapsto (\Psi(f))(x) = \int_0^x\!f(y)\,\mathrm{d}y
\end{alignat*}

\end{document}

Answer 3

Nest aligned[t] inside aligned inside equation.

I provide two realizations; in the bottom one there are a couple of improvements:

1. the arrows are shorter (and nicer);
2. the parentheses around [0,1],\RR are a bit larger.

Why \RR instead of \mathbb{R}? Because the real numbers are a specific symbol for your document and you want to ensure consistent typesetting. As a bonus, if your coauthor comes up with a different way of typesetting the set of real numbers (and other number sets), you can just modify the definition of \numberset.

Similarly, by defining \diff for the “differential d”, you can ensure consistent typesetting without the need of remembering to add \,. You can change d in the definition to \mathrm{d} if you (or your coauthor) really want an upright “d” (I fervently hope not 😀).

\documentclass{article}
\usepackage{amsmath}
\usepackage{amssymb}

\newcommand{\numberset}[1]{\mathbb{#1}}% generic
\newcommand{\RR}{\numberset{R}}% specific

\newcommand{\diff}{\mathop{}\!d}

\begin{document}

\begin{equation*}
\begin{aligned}
  \Psi\colon C([0,1],\RR) &\longrightarrow C([0,1],\RR) \\ 
  f & \longmapsto 
  \begin{aligned}[t]
    \Psi(f)\colon [0,1] & \longrightarrow \RR \\
                  x     & \longmapsto (\Psi(f))(x)=\int_0^x f(y) \diff y
  \end{aligned}
\end{aligned}
\end{equation*}

\begin{equation*}
\begin{aligned}
  \Psi\colon C\bigl([0,1],\RR\bigr) &\rightarrow C\bigl([0,1],\RR\bigr) \\ 
  f & \mapsto 
  \begin{aligned}[t]
    \Psi(f)\colon [0,1] & \rightarrow \RR \\
                  x     & \mapsto (\Psi(f))(x)=\int_0^x f(y)\diff y
  \end{aligned}
\end{aligned}
\end{equation*}

\end{document}