How can I type the symbol for usual topology $R_{(-)}$ in LaTex?

Sigur's answer might be appealing, but it has a big defect: with \usepackage{MnSymbol} you change every math symbol in your document to shapes that are thought to accompany Minion.

Besides, I find the strokes in MnSymbol to be too heavy. Your symbol should be as less intrusive as possible. How to use MnSymbol without all these defects?

\documentclass{article}
\usepackage{amsmath,amssymb}

% from MnSymbol.sty
\DeclareFontFamily{U}{MnSymbolA}{}
\DeclareFontShape{U}{MnSymbolA}{m}{n}{
    <-6>  s*[0.7] MnSymbolA5
   <6-7>  s*[0.7] MnSymbolA6
   <7-8>  s*[0.7] MnSymbolA7
   <8-9>  s*[0.7] MnSymbolA8
   <9-10> s*[0.7] MnSymbolA9
  <10-12> s*[0.7] MnSymbolA10
  <12->   s*[0.7] MnSymbolA12}{}

\DeclareRobustCommand{\usual}{%
  \text{\usefont{U}{MnSymbolA}{m}{n}\ooalign{\char"80\cr\char"82\cr}}%
}

\begin{document}

$\mathbb{R}_{\usual}$

\end{document}

Explanation: MnSymbol tells us that the required symbols are from MnSyA that's defined as a math symbol font in the package itself. So it's easy to borrow the font definitions and adding a scale factor to make the glyph smaller.

The font table reveals that the two symbols are at positions "80 and "82 respectively, so we can use them in \ooalign that superimposes them inside \text, without wasting a math font family.

Another possibility, cutting out the parenthesis from a \bigcirc to get more round symbols. To get a more similar symbols with square brackets, I cut them out of amssymb's \square.

\documentclass{article}
\usepackage{mathtools}
\usepackage{amssymb}
\usepackage{trimclip}
\newcommand{\leftparen}{\clipbox{0 0 5.5pt 0}{\(\scriptstyle\bigcirc\)}}
\newcommand{\rightparen}{\clipbox{5.5pt 0 0 0}{\(\scriptstyle\bigcirc\)}}
\newcommand{\leftsquare}{\raisebox{-.9pt}{\clipbox{0 0 4.5pt 0}{\(\scriptstyle\square\)}}}
\newcommand{\rightsquare}{\raisebox{-.9pt}{\clipbox{4.5pt 0 0 0}{\(\scriptstyle\square\)}}}
\newcommand{\leftrightopen}{\mathrlap{\leftparen}-\!\!-\mathllap{\rightparen}}
\newcommand{\leftrightclosed}{\mathrlap{\leftsquare}-\!\!-\mathllap{\rightsquare}}
\newcommand{\Rtopopen}{\mathbb{R}_{\leftrightopen}}
\newcommand{\Rtopoclosed}{\mathbb{R}_{\leftrightclosed}}
\begin{document}
\( \Rtopopen \qquad \Rtopoclosed \)
\end{document}

Just because a tikz answer is always required ... Here is one using the Arc Barb arrowhead style of the arrows.meta library.

EDIT Added a line cap=round option to show that you can pretty much customize the shape as you need.

\documentclass{article}
\usepackage{amssymb}
\usepackage{tikz}
\usetikzlibrary{arrows.meta}

\newcommand{\topo}{%
    {\tikz {
        \draw[<->,>={Arc Barb[length=0.15em,width=1ex]}] (0,0) -- (0.7em,0); 
    }}%
}
\newcommand{\toporound}{%
    {\tikz {
        \draw[<->,>={Arc Barb[length=0.15em,width=1ex,line cap=round]}] (0,0) -- (0.7em,0); 
    }}%
}

\begin{document}
    $ \mathbb{R}_\topo$ $ \mathbb{R}_\toporound$
\end{document}