Kernel of a set

2020 Mathematics Subject Classification: Primary: 54A [MSN][ZBL]

open kernel of a set $M$

The set $\langle M \rangle$ of all interior points of $M$, cf. Interior point of a set. If $A$ and $B$ are mutually complementary sets in a topological space $X$, that is, if $B = X \setminus A$, then $X \setminus [A] = \langle B \rangle$ and $X \setminus \langle B \rangle = [ A ]$, where $[A]$ denotes the closure of $A$ (cf. Closure of a set).

Comments

$\langle M \rangle$ is usually called the interior of $M$ (cf. Interior of a set), and is also denoted by $M^\circ$ and $\mathrm{Int}\, M$. The word "kernel" is seldom used in the English mathematical literature in this context.