Closure under a binary operation
= Closure under a binary operation
{title2=$a,b\in A\implies a\ast b\in A$}
A <subset> $A\subseteq S$ is closed under a <binary operation> on $S$ when the result of combining any two elements of $A$ is again in $A$. The <even integers> are closed under <addition>, but the <odd integers> are not: $1+3=4$ is even. Closure permits restricting the <binary operation> to $A\times A\to A$. It is different from being a <closed set> in <topology>.