Join (topology)
In topology, a field of mathematics, the join of two topological spaces A {\displaystyle A} and B {\displaystyle B} , often denoted by A ∗ B {\displaystyle A\ast B} or A ⋆ B {\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 A {\displaystyle A} to every point in B {\displaystyle B} . The join of a space A {\displaystyle A} with itself is denoted by A ⋆ 2 := A ⋆ A {\displaystyle A^{\star 2}:=A\star A} .