regular

Regular point

For a smooth map $F:M\to N$, a point $x\in M$ is called regular if $F$ is a submersion at $x$. In other words, if ${\text{rank}}_x(F)=\dim N$, for the rank of the smooth map.

Regular set

Given the same setup as above, a set $U\subset M$ is called regular if every point $x\in U$ is a regular point.