Subscript under subset sign

Question

How can one achieve a sub-index and super-index over a subset sign, as in the following image:

I have not found any resources online. Thanks!

Answer 1

\mathop{\subset}_{t=x}^{t=y} will give the limits layout you show in display math.

Answer 2

You could use \DeclareMathOperator* from the amsmath package. That way you get the indices above and below only in display mode, not inline so the spacing between lines is not affected.

\documentclass{article}
\usepackage{amsmath}
\DeclareMathOperator*{\isubset}{\subset}
\begin{document}
[
\isubset_{t=x}^{t=y} f(t,\vec x, \vec\alpha)
]
Inline: $\isubset_{t=x}^{t=y} f(t,\vec x, \vec\alpha)$.
\end{document}

Answer 3

I'd rotate \bigcup.

\documentclass{article}
\usepackage{amsmath}
\usepackage{graphicx}
\makeatletter
\DeclareRobustCommand{\bigsubset}{%
  \DOTSB\mathop{\bigsubsupset@{\bigcup}}\slimits@
}
\DeclareRobustCommand{\bigsupset}{%
  \DOTSB\mathop{\bigsubsupset@{\bigcap}}\slimits@
}
\newcommand{\bigsubsupset@}[1]{\mathpalette\bigsubsupset@@{#1}}
\newcommand{\bigsubsupset@@}[2]{%
  \vphantom{\sum}% vertical space
  \vcenter{\hbox{\rotatebox[origin=c]{-90}{$\m@th#1#2$}}}
  \ifx#1\displaystyle\else,\fi
}
\makeatother
\begin{document}
[
A



\sum_{t=x}^{t=y}f(t,\vec{x},\vec{a})



\bigsubset_{t=x}^{t=y}f(t,\vec{x},\vec{a})



\bigsupset_{t=x}^{t=y}f(t,\vec{x},\vec{a})
]
\begin{center}
$
A



\sum_{t=x}^{t=y}f(t,\vec{x},\vec{a})



\bigsubset_{t=x}^{t=y}f(t,\vec{x},\vec{a})



\bigsupset_{t=x}^{t=y}f(t,\vec{x},\vec{a})
$
\end{center}
\end{document}

Without \vphantom{\sum} you'd get