If the preferred math font does not contain the symbol, it can be provided by putting \cup
and \cdot
together:
\documentclass{article}
\usepackage{amsmath}
\makeatletter
\providecommand*{\cupdot}{%
\mathbin{%
\mathpalette\@cupdot{}%
}%
}
\newcommand*{\@cupdot}[2]{%
\ooalign{%
$\m@th#1\cup$\cr
\hidewidth$\m@th#1\cdot$\hidewidth
}%
}
\makeatother
\begin{document}
\[ a\cupdot b\]
\end{document}

Remarks:
\mathbin
keeps the spacing of a binary operator (like \cup
) for the new symbol.
- The trick with
\mathpalette
ensures that the symbol adopts its size if used in fractions, subscripts, ...
Variant with vertically centered dot and \bigcupdot
\documentclass{article}
\usepackage{amsmath}
\usepackage{graphicx}
\makeatletter
\providecommand*{\cupdot}{%
\mathbin{%
\mathpalette\@cupdot{}%
}%
}
\newcommand*{\@cupdot}[2]{%
\ooalign{%
$\m@th#1\cup$\cr
\sbox0{$#1\cup$}%
\dimen@=\ht0 %
\sbox0{$\m@th#1\cdot$}%
\advance\dimen@ by -\ht0 %
\dimen@=.5\dimen@
\hidewidth\raise\dimen@\box0\hidewidth
}%
}
\providecommand*{\bigcupdot}{%
\mathop{%
\vphantom{\bigcup}%
\mathpalette\@bigcupdot{}%
}%
}
\newcommand*{\@bigcupdot}[2]{%
\ooalign{%
$\m@th#1\bigcup$\cr
\sbox0{$#1\bigcup$}%
\dimen@=\ht0 %
\advance\dimen@ by -\dp0 %
\sbox0{\scalebox{2}{$\m@th#1\cdot$}}%
\advance\dimen@ by -\ht0 %
\dimen@=.5\dimen@
\hidewidth\raise\dimen@\box0\hidewidth
}%
}
\makeatother
\begin{document}
\[ \bigcupdot a\cupdot b\]
\end{document}
\documentclass{article}
\usepackage{amsmath}
\makeatletter
\providecommand*{\cupdot}{%
\mathbin{%
\mathpalette\@cupdot{}%
}%
}
\newcommand*{\@cupdot}[2]{%
\ooalign{%
$\m@th#1\cup$\cr
\sbox0{$#1\cup$}%
\dimen@=\ht0 %
\sbox0{$#1\cdot$}%
\advance\dimen@ by -\ht0 %
\dimen@=.5\dimen@
\hidewidth\raise\dimen@\hbox{$\m@th#1\cdot$}\hidewidth
}%
}
\makeatother
\begin{document}
\[ \bigcupdot_{i=1}^{\infty} a_i\cupdot b \]
\end{document}

amssymb
. But you can build one yourself: tex.stackexchange.com/a/52673/21591