How to prevent amsmath's \dots from adding extra space to a custom \set macro?

Question

I've written a custom \set macro to typeset sets allowing line breaks at every comma:

\documentclass{article}
\usepackage[T1]{fontenc}
%\usepackage{amsmath} %<-- (un)comment to toggle the problem


% this is the colon in expressions like {n : n < 10}
\newcommand*{\setgiven}[1][]{%              #1 is discarded
  \nonscript\medspace\mathord:\allowbreak%  medspace? + : + break?
  \nonscript\medspace\mathopen{}%           medspace?
}

% \parseset splits a comma-separated list like
% 1,2,3,4,5
% into a sequence stored in \g_setlist_seq
\ExplSyntaxOn
\seq_new:N \g_setlist_seq
\cs_new_nopar:Npn \parseset #1 {
  \seq_set_split:Nnn \g_setlist_seq { , } { #1 }
}
% \printset prints list \g_setlist_seq with
% each element separated by  ,\allowbreak
\cs_new_nopar:Npn \printset {
  \seq_use:Nnnn \g_setlist_seq {,\allowbreak}{,\allowbreak}{,\allowbreak}
}
\ExplSyntaxOff

\NewDocumentCommand{\set}{s o m}{%
  % \set{1,2,3} => simple set that allows line breaks at commas
  % \set[n]{n<10} => {n : n < 10}
  % the starred versions use \left\{ and \right\} to handle "tall" characters
  \parseset{#3}%
  \IfValueTF{#2}  % WITH optional argument
  {\IfBooleanTF{#1}  % starred: \left and \right
    {\left\lbrace #2\setgiven[\delimsize] \printset \right\rbrace}%
    {\lbrace #2\setgiven[\delimsize] \printset \rbrace}%
  }
  % WITHOUT optional argument
  {\IfBooleanTF{#1}  % starred: \left and \right
    {\left\lbrace \printset \right\rbrace}
    {\lbrace \printset \rbrace}%
  }%
}


\begin{document}

\begin{tabular}{r l}
  With \string\mathellipsis & $\set{1, 2, \mathellipsis}$\\
  With \string\dots & $\set{1, 2, \dots}$\\
  %With \string\dotsc & $\set{1, 2, \dotsc}$\\ %<-- uncomment when using amsmath
  With \string\dots\string\relax & $\set{1, 2, \dots\relax}$\\
  With \string\dots\{\} & $\set{1, 2, \dots{}}$
\end{tabular}

\end{document}

This macro should behave well with amsmath, because it's a very common package. It's also very common to write sets such as \set{1, 2, \dots}, so the macro should also behave well with \dots at the end.

I've found out that while the macro is ok with standard LaTeX, ending a \set with \dots adds some extra space if you're using amsmath (\dots in the middle of other things, as in \set{1, \dots, n}, is fine).

Regular LaTeX:

With amsmath:

After examining amsmath.sty and reading a few questions here, I know the amsmath version of \dots examines the next token to decide which kind of dots to use, but I don't know why in this case it adds extra space.

There's a way to prevent this, using something else at the end of a \set: \dots\relax and \mathellipsis work, but \dots{} and \dotsc don't (which is not very intuitive, I think people would expect all four of these to work).

So, is there a way to allow a user using amsmath to simply type \dots and don't get the extra space?

Answer 1

as you show a trailing \relax is enough, so you can supply one, it won't affect anything apart from this lookahead.

  \parseset{#3\relax}%
              %%%%%%