8

I'm reading about inverse limits, and the notation sometimes requires some sort of index or set over which to take the inverse limit. It looks something like this:

enter image description here

How would I correctly TeX that? I tried something like {\lim_{\longleftarrow}}_{H\in\mathscr{F}} but the arrow and the set are side by side, not one over the other.

yunone
  • 3,259

5 Answers5

11

There is no need for \substack in this case: there are the \varinjlim and \varprojlim macros taking care of both direct and inverse limits, putting a subscript now results in the behaviour you're looking for (and everyone is mimicking using \substack).

Pieter
  • 5,411
  • Thanks Pieter, I didn't know such macros existed. Just was I was looking for. – yunone Aug 19 '11 at 19:19
  • @Pieter: You're right. Use \usepackage{mathtools} and then \underset{i}{\varinjlim} for inverse limit, and \underset{H\in\mathscr{F}}{\varprojlim} for direct limit (the latter requires \usepackage{mathrsfs} as well). – Werner Aug 19 '11 at 19:28
  • @Werner He needs \varprojlim when reproducing the examples, inverse limits are also known as projective limits. And why use \underset? Just \varprojlim_i will do fine, even in text style where it is appropriate for the limit to be on the right. – Pieter Aug 19 '11 at 19:33
  • @Pieter: You're right, again... – Werner Aug 19 '11 at 19:39
3

Without going into too much font detail, you can use the \mathop{<stuff>} command to make an operator of almost anything in mathmode. For example, here's a small modification to your initial try:

\mathop{\lim_{\longleftarrow}}_{i}G/H_i \approx
  \mathop{\lim_{\longleftarrow}}_{H\in\mathcal{F}}G/H

Mathop to define mathematical operators with limits

However, you may also be interested in stacking items on top of one another using \stackrel{<top>}{<bottom>}:

\lim_{\stackrel{\longleftarrow}{i}}G/H_i \approx
  \lim_{\stackrel{\longleftarrow}{H\in\mathcal{F}}}G/H

Stacking limits using \stackrel

Consider browsing through Herbert Voß' mathmode document. It is filled with typesetting information in mathmode.

Werner
  • 603,163
  • @yunone: It does modify the fontsize slightly for the <upper> part. In this case \longleftarrow; that's why you see it being slightly shorter. – Werner Aug 19 '11 at 18:56
3

You could use \substack of amsmath:

\lim_{\substack{\longleftarrow\\H\in\mathscr{F}}}

substack example

Stefan Kottwitz
  • 231,401
2
\documentclass{article}
\usepackage{mathtools}
\begin{document}

\[ \lim_{\xleftarrow[i]{}}G/H_i \approx
   \lim_{\xleftarrow[\mathclap{H\in\mathcal{F}}]{}}G/H \]

\end{document}

enter image description here

0

You can define a new operator using \DeclareMathOperator of the amsmath package as follows:

\documentclass{article}

\usepackage{mathtools}

\DeclareMathOperator*{\ulalim}{\underleftarrow\lim}

\begin{document}

\[\ulalim_{i}G/H_{i}\approx\smashoperator{\ulalim_{H\in\mathcal{F}}}G/H\]

\end{document}

The resulting output is:

Note the usage of \smashoperator to remove redundant white space between the operator and the operand on the right-hand side of the equation.

mhp
  • 8,692
  • OK, in this specific case, you actually don't need to define a new operator since there is already one as pointed out by @Pieter. – mhp Aug 19 '11 at 20:09