\documentclass[12pt,a4paper,notitlepage]{report}
\usepackage[cp1251]{inputenc}
\usepackage[T1,T2A]{fontenc}
\usepackage[russian]{babel}
\usepackage{amsmath, amssymb}
\usepackage{mathrsfs}
\usepackage{enumitem}
\usepackage{relsize}
\usepackage{exscale}
\usepackage{perpage}
\usepackage{nicefrac}
\usepackage[all,cmtip]{xy}
\MakePerPage{footnote}
\newcommand{\LBR}{
\hspace{0.2em}\rule[0.75em]{0.2em}{0.05em}% top serif
\hspace{-0.2em}\rule[-0.2em]{0.2em}{0.05em}% bottom serif
\hspace{-0.3em}\rule[-0.2em]{0.1em}{1.0em}% vertical bar
\hspace{0.2em}
}
\newcommand{\RBR}{
\hspace{0.1em}\rule[0.75em]{0.2em}{0.05em}% top serif
\hspace{-0.2em}\rule[-0.2em]{0.2em}{0.05em}% bottom serif
\rule[-0.2em]{0.1em}{1.0em}% vertical bar
\hspace{0.2em}
}
\newcommand{\opni}[1] {{\RBR #1 \LBR}}
\newcommand{\opcli}[1]{{\RBR #1 \RBR}}
\newcommand{\clopi}[1]{{\LBR #1 \LBR}}
\newcommand{\clsi}[1] {{\LBR #1 \RBR}}
\begin{document}
\[
\begin{array}{ll}
\opni{a, b} &=\ \{x\in A: a < x < b\},\\
\opcli{a, b} &=\ \{x\in A: a < x\leqslant b\},\\
\clopi{a, b} &=\ \{x\in A: a\leqslant x < b\},\\
\clsi{a, b} &=\ \{x\in A: a\leqslant x\leqslant b\},\\
\opni{{\gets},a} &=\ \{x\in A: x < a\},\\
\opcli{{\gets},a} &=\ \{x\in A: x\leqslant a\},\\
\opni{a,{\to}} &=\ \{x\in A: a < x\},\\
\clopi{a,{\to}} &=\ \{x\in A: a\leqslant x\}.
\end{array}
\]
$\mathbb{R}^\clsi{a,b}$
\end{document}
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