Import empty set from Computer Modern font

Question

I use \mathabx package because I like much more their mathematical symbols. Except for the empty set symbol ($\emptyset$ in LaTeX). I would like to changed it by the standard Computer Modern symbol. But I don't know how to do it. There are some examples to import particular symbols, but I don't undertsand them.

For example, the code

\DeclareFontFamily{U}{matha}{\hyphenchar\font45}
\DeclareFontShape{U}{matha}{m}{n}{
      <5> <6> <7> <8> <9> <10> gen * matha
      <10.95> matha10 <12> <14.4> <17.28> <20.74> <24.88> matha12
      }{}
\DeclareSymbolFont{matha}{U}{matha}{m}{n}
\DeclareFontSubstitution{U}{matha}{m}{n}
\DeclareMathSymbol{\abxcup}{\mathbin}{matha}{'131}

has been taken from the question The standard \cup vs. the mathabx \cup. Question Importing a Single Symbol From a Different Font also has a similar code. How can I changed them to get the standard empty set symbol?

Thanks

Answer 1

For completeness, I provide the original solution, on the assumption that the font needed is not already loaded by TeX. Afterward, I show a streamlined solution, since cmsy (Computer Modern symbol font family) has already been loaded by default.

The Long Way:

Here, after mathabx is loaded, I declare and define the cmsy font family, found on p.431 of the TeXbook. cmsy is the name that the Computer Modern symbol font family is known as, to TeX. It is called a font "family" because the font is provided in different sizes, and \DeclareFontShape tells which glyph set (member of the family) to use depending on the fontsize that is requested.

I create a new symbol font Xcmsy that points to the cmsy font family. I then declare the symbol \cmemptyset to be of categorymathord, and found in slot 59 of the Xcmsy font.

If you uncomment the two fonttable lines of code, you will see the cmsy font printed out in tabular form, and can verify that the empty set glyph is found at slot 59.

\documentclass{article}
\usepackage{mathabx}
% =============================================
%Import symbols from font cmsy without importing the whole package
% =============================================
\DeclareFontFamily{U} {cmsy}{}

\DeclareFontShape{U}{cmsy}{m}{n}{
  <-8> cmsy7
  <8-9> cmsy8
  <9-10> cmsy9
  <10-> cmsy10}{}

\DeclareSymbolFont{Xcmsy} {U} {cmsy}{m}{n}

\DeclareMathSymbol{\cmemptyset}{\mathord}{Xcmsy}{59}
% =============================================
%\usepackage{fonttable}
\begin{document}
\centering

$\emptyset \cmemptyset$ 

%\tiny\fonttable{cmsy8}
\end{document}

The Short Way (for Computer Modern only):

Because Computer Modern is already loaded by TeX as the default font, much of the prior method is redundant and the answer can be streamlined (as noted by GuM):

\documentclass{article}
\usepackage{mathabx}
% =============================================
\DeclareMathSymbol{\cmemptyset}{\mathord}{symbols}{59}
% =============================================
\begin{document}
\centering

$\emptyset \cmemptyset$ 

\end{document}

Answer 2

The answer below is inspired by the way the author of the mathabx package, Anthony Phan, uses to retain the old \emptyset symbol (which he calls \voidset) while loading his mathabx package (see the TeX source of its documentation).

\documentclass{article}
\let\voidset=\emptyset
\usepackage{mathabx}
\let\emptyset=\voidset
\begin{document} 
$\emptyset$   
\end{document}

Answer 3

\emptyset using package cancel.

\documentclass{article}
\usepackage{cancel, amsmath}
\usepackage{amssymb, mathabx} 
\begin{document}
\( \cancel{\bigcirc} \)
\end{document}