Mathematical symbol for disjoint set union

Question

In our lecture script, we use the notion of disjoint set union. It uses a special symbol to differentiate the disjoint from the usual set union, where we add an extra dot inside of the \cup symbol. Is there something like a \bigudot? Or any other way to add a centered dot to any symbol?

Answer 1

Edit I thought amssymb provides \cupdot which does what you want... but it doesn't.

\usepackage{MnSymbol} provides \cupdot and \bigcupdot but is incompatible with amssymb which is unfortunate.

Sometimes disjoint union is depicted using \sqcup which has the advantage of being in amssymb

Answer 2

Another possibility to go around the problem that there is no such symbol in amssymb is to use the dot-accent: \dot{\bigcup} or also \dot\bigcup. This works for all symbols, and might very well be the reason that there are no dotted symbols in amssymb.

To let TeX treat such a new construct as an operator in terms of spacing though, you need to use \mathop and \mathbin, that's to say \mathop{\dot{\bigcup}} and \mathbin{\dot{\cup}}.

Answer 3

Disjoint union is also sometimes written using \coprod, since it is in fact the coproduct in the category of sets.

Answer 4

Another way is the following:

\makeatletter
\def\moverlay{\mathpalette\mov@rlay}
\def\mov@rlay#1#2{\leavevmode\vtop{%
   \baselineskip\z@skip \lineskiplimit-\maxdimen
   \ialign{\hfil$\m@th#1##$\hfil\cr#2\crcr}}}
\newcommand{\charfusion}[3][\mathord]{
    #1{\ifx#1\mathop\vphantom{#2}\fi
        \mathpalette\mov@rlay{#2\cr#3}
      }
    \ifx#1\mathop\expandafter\displaylimits\fi}
\makeatother

\newcommand{\cupdot}{\charfusion[\mathbin]{\cup}{\cdot}}
\newcommand{\bigcupdot}{\charfusion[\mathop]{\bigcup}{\cdot}}

The \charfusion macro is built on \moverlay (by D. Arseneau).

Examples:

$A\cupdot B$

\[ \bigcupdot_{i\in I} A_{i} \]

Answer 5

A redacted version from symbols:

\newcommand{\cupdot}{\mathbin{\mathaccent\cdot\cup}}

This shows @egreg's solution, "my" solution, and @Vilietha's solution side by side:

Not much difference between egreg's and mine, but maybe less to type ;-)

Answer 6

If you use xelatex and unicode-math you can simply use the symbol ⊍ directly, or its alias \cupdot: $A ⊍ B \cupdot C$ renders with XITS Math as .

Answer 7

Here it is another way though dot not inside but above the cup:

$A \overset{\cdot}{\cup} B$

I would put plus instead of dot! would look nicer!

Answer 8

The easiest way to do the dot inside union is

\cdot \hspace{-12pt}\bigcup