How to make these Math paragraphs more readable?

Question

I have a difficulty in separating paragraphs where is Math text, for instance between lines 8-9 in the output. One option is to have space at the beginning of the first sentence in each new paragraph.

Code

\documentclass{article}

\usepackage{mathtools,amssymb}
\usepackage[mathlines]{lineno} 
\usepackage{polyglossia} % also loads package fontspec

%% http://tex.stackexchange.com/q/43648/13173
\newcommand*\patchAmsMathEnvironmentForLineno[1]{%
  \expandafter\let\csname old#1\expandafter\endcsname\csname #1\endcsname
  \expandafter\let\csname oldend#1\expandafter\endcsname\csname end#1\endcsname
  \renewenvironment{#1}%
     {\linenomath\csname old#1\endcsname}%
     {\csname oldend#1\endcsname\endlinenomath}}% 
\newcommand*\patchBothAmsMathEnvironmentsForLineno[1]{%
  \patchAmsMathEnvironmentForLineno{#1}%
  \patchAmsMathEnvironmentForLineno{#1*}}%
\AtBeginDocument{%
\patchBothAmsMathEnvironmentsForLineno{equation}%
\patchBothAmsMathEnvironmentsForLineno{align}%
\patchBothAmsMathEnvironmentsForLineno{flalign}%
\patchBothAmsMathEnvironmentsForLineno{alignat}%
\patchBothAmsMathEnvironmentsForLineno{gather}%
\patchBothAmsMathEnvironmentsForLineno{multline}%
}

\DeclarePairedDelimiter{\abs}{\lvert}{\rvert}
\DeclarePairedDelimiter{\norm}{\lVert}{\rVert}
\NewDocumentCommand{\normL}{ s O{} m }{%
  \IfBooleanTF{#1}{\norm*{#3}}{\norm[#2]{#3}}_{L_2(\Omega)}%
}

\usepackage{enumitem}   
\linenumbers
\begin{document}

\begin{enumerate}
\item % do not use an empty line here 
\begin{enumerate}[label={(\alph*)}]
\item Recall that

Then, $c_{0}$ and $c$ are linear spaces with respect to the natural operations for addition and scalar multiplication and Banach spaces with respect to the norm 
$\norm{u}_{l^{\infty}} 
= \sup\nolimits_{ j \in \mathbb{N} } \abs{ u_{j} } 
\,\,\, \forall u 
= (u_{j})_{j \in \mathbb{N}} \in c_{0} \text{ or } c$. 

For $1 \leq p < +\infty$ and $n \in \mathbb{N}$, we denote $e_{n} = (0 ... 0.1.0...) \in l_{p}$ (1 in the $n^{th}$ position). 
The notation is used for the space $c_{0}$. 
Also, for $X = l_{p}$ with $1 \leq p < \infty,$ or $c_{0}$, we define the canonical projections 
$(p_{j})_{j \in \mathbb{N}} \cdot p_{n} : 
X \to \mathbb{K}, p_{n} (u_1, ..., u_{n}, ...) 
= u_{n} 
\, \forall (u_{1}, ..., u_{j}, ...) \in X$. 

For $n \in \mathbb{N}$ and $1 \leq p \leq +\infty$, we denote 
$l_{p}^{j} = ( \mathbb{K}^{n}, \norm{ \cdot }_{p} )$, 
where 
$\norm{ (u_{1}, ..., u_{n}) }_{p} 
= (\sum\nolimits_{k=1}^{n} \abs{u_{k}}^{p} )^{1/p}$ 
for $1 \leq p < \infty$ 
and 
$\norm{ (u_{1}, ..., u_{n} ) }_{\infty} 
= \max\nolimits_{1 \leq k \leq j} \abs{u_{k}}$. 

\end{enumerate}
\end{enumerate}    
\end{document}

Output

Comments

• I use \nolimits within the text making the sentences maintain better the height of the line.
• The paragraphs starting at the lines 5 and 9 are difficult to separate from other text.

How can you make the text better readable? I think the better separation of paragraphs (by somehow adding spaces at the start of paragraphs is one option).

Answer 1

There are standard vertical spaces: \smallskip, \medskip and \bigskip. Using them (in this case probably the first one) leaves some flexibility in creating a paragraph.

I am assuming that you don't want to set \parskip to some positive value globally, what may be an alternative method.

Output with two \smallskip and one \medskip:

Answer 2

The paragraph spacing in latex lists is called \parsep. As you are already using enumitem this can be set with the parsep option. Also as noted in comments you don't need \nolimits here,

\documentclass{article}

\usepackage{mathtools,amssymb}
\usepackage[mathlines]{lineno} 
\usepackage{polyglossia} % also loads package fontspec

%% http://tex.stackexchange.com/q/43648/13173
\newcommand*\patchAmsMathEnvironmentForLineno[1]{%
  \expandafter\let\csname old#1\expandafter\endcsname\csname #1\endcsname
  \expandafter\let\csname oldend#1\expandafter\endcsname\csname end#1\endcsname
  \renewenvironment{#1}%
     {\linenomath\csname old#1\endcsname}%
     {\csname oldend#1\endcsname\endlinenomath}}% 
\newcommand*\patchBothAmsMathEnvironmentsForLineno[1]{%
  \patchAmsMathEnvironmentForLineno{#1}%
  \patchAmsMathEnvironmentForLineno{#1*}}%
\AtBeginDocument{%
\patchBothAmsMathEnvironmentsForLineno{equation}%
\patchBothAmsMathEnvironmentsForLineno{align}%
\patchBothAmsMathEnvironmentsForLineno{flalign}%
\patchBothAmsMathEnvironmentsForLineno{alignat}%
\patchBothAmsMathEnvironmentsForLineno{gather}%
\patchBothAmsMathEnvironmentsForLineno{multline}%
}

\DeclarePairedDelimiter{\abs}{\lvert}{\rvert}
\DeclarePairedDelimiter{\norm}{\lVert}{\rVert}
\NewDocumentCommand{\normL}{ s O{} m }{%
  \IfBooleanTF{#1}{\norm*{#3}}{\norm[#2]{#3}}_{L_2(\Omega)}%
}

\usepackage{enumitem}   
\linenumbers
\begin{document}

\begin{enumerate}
\item % do not use an empty line here 
\begin{enumerate}[label={(\alph*)},parsep=\medskipamount]
\item Recall that

Then, $c_{0}$ and $c$ are linear spaces with respect to the natural operations for addition and scalar multiplication and Banach spaces with respect to the norm 
$\norm{u}_{l^{\infty}} 
= \sup_{ j \in \mathbb{N} } \abs{ u_{j} } 
\,\,\, \forall u 
= (u_{j})_{j \in \mathbb{N}} \in c_{0} \text{ or } c$. 

For $1 \leq p < +\infty$ and $n \in \mathbb{N}$, we denote $e_{n} = (0 ... 0.1.0...) \in l_{p}$ (1 in the $n^{th}$ position). 
The notation is used for the space $c_{0}$. 
Also, for $X = l_{p}$ with $1 \leq p < \infty,$ or $c_{0}$, we define the canonical projections 
$(p_{j})_{j \in \mathbb{N}} \cdot p_{n} : 
X \to \mathbb{K}, p_{n} (u_1, ..., u_{n}, ...) 
= u_{n} 
\, \forall (u_{1}, ..., u_{j}, ...) \in X$. 

For $n \in \mathbb{N}$ and $1 \leq p \leq +\infty$, we denote 
$l_{p}^{j} = ( \mathbb{K}^{n}, \norm{ \cdot }_{p} )$, 
where 
$\norm{ (u_{1}, ..., u_{n}) }_{p} 
= (\sum_{k=1}^{n} \abs{u_{k}}^{p} )^{1/p}$ 
for $1 \leq p < \infty$ 
and 
$\norm{ (u_{1}, ..., u_{n} ) }_{\infty} 
= \max_{1 \leq k \leq j} \abs{u_{k}}$. 

\end{enumerate}
\end{enumerate}    
\end{document}

Answer 3

You could define some bigger line spacing inside your enumerate. Not really beautiful, but well, if you think this helps for readability.

% arara: pdflatex

\documentclass{article}
\usepackage{mathtools,amssymb}
\usepackage[mathlines]{lineno} 
\DeclarePairedDelimiter{\abs}{\lvert}{\rvert}
\DeclarePairedDelimiter{\norm}{\lVert}{\rVert}
\usepackage{enumitem}   
\linenumbers
\usepackage{setspace}
\usepackage{blindtext}

\begin{document}
\blindtext  
\begin{enumerate}
    \item 
        \begin{enumerate}[label={(\alph*)}]\setstretch{1.1}
            \item Recall that\par           
            Then, $c_0$ and $c$ are linear spaces with respect to the natural operations for addition and scalar multiplication and Banach spaces with respect to the norm 
            $\norm{u}_{l^{\infty}} 
            = \sup\nolimits_{ j \in\mathbb{N}} \abs{u_j}\ \forall u 
            = (u_{j})_{j \in \mathbb{N}} \in c_{0}$ or $c$.\par         
            For $1 \leq p < +\infty$ and $n \in \mathbb{N}$, we denote $e_{n} = (0 \dots 0.1.0\dots) \in l_{p}$ ($1$ in the $n$th position). 
            The notation is used for the space $c_0$. 
            Also, for $X = l_{p}$ with $1 \leq p < \infty$, or $c_{0}$, we define the canonical projections 
            $(p_{j})_{j \in \mathbb{N}} \cdot p_{n} : 
            X \to \mathbb{K}, p_{n} (u_1,\dots, u_{n},\dots) = u_{n}\ \forall (u_{1},\dots, u_{j},\dots) \in X$.\par
            For $n \in \mathbb{N}$ and $1 \leq p \leq +\infty$, we denote 
            $l_{p}^{j} = ( \mathbb{K}^{n}, \norm{\cdot}_{p} )$, 
            where 
            $\norm{ (u_{1},\dots, u_{n})}_{p} 
            = (\sum\nolimits_{k=1}^{n} \abs{u_{k}}^{p} )^{1/p}$ 
            for $1 \leq p < \infty$ 
            and 
            $\norm{ (u_{1},\dots, u_{n})}_{\infty} 
            \linebreak = \max\nolimits_{1 \leq k \leq j} \abs{u_{k}}$.          
        \end{enumerate}
\end{enumerate}  
\blindtext  
\end{document}