In topology, a field of mathematics, the join of two topological spaces ${\displaystyle A}$ and ${\displaystyle B}$, often denoted by ${\displaystyle A\ast B}$ or ${\displaystyle A\star B}$, is a topological space formed by taking the disjoint union of the two spaces, and attaching line segments joining every point in ${\displaystyle A}$ to every point in ${\displaystyle B}$. The join of a space ${\displaystyle A}$ with itself is denoted by ${\displaystyle A^{\star 2}:=A\star A}$. The join is defined in slightly different ways in different contexts