How to prevent a math symbol to change its type [relation, operator etc.] and modify the space around?

Question

Typically, we take \leq:

\documentclass{article}

\begin{document}
    \[     \leq \simeq \leq_A \sim  \leq_B     \]

    \[         \leq \simeq {\leq_A} \sim  {\leq_B}     \]

\end{document}

and see the space around the two \sim is not respected as soon as we put a subletter on them Why does tex do that ? How to prevent it without having to put the braces around each new symbol or use a command to define leq taking an input?

Answer 1

Both \[ \leq \simeq \leq \sim \leq \] and \[ \leq \simeq \leq_A \sim \leq_B \] lead to similar results when it comes to spacing as all of the symbols are treated as relations.

Putting curly braces around \leq_A, so it becomes {\leq_A}, results in {\leq_A} switching its type from mathrel to mathord (see What is the difference between \mathbin vs. \mathrel?); so LaTeX treats {\leq_A} \sim {\leq_B} as any ordinary symbol just like a \sim b.

What to do really depends on the meaning of your input. If you want to establish a binary relation between \leq_A and \leq_B with \sim (let's say: equivalence of two binary relations) just like a relation between a and b, you need to wrap \leq_A and \leq_B in curly braces or \mathord, define a new command for that if you need it more often. If you want \leq \simeq \leq_A \sim \leq_B to act like one massive relation, just leave it as it is.