final topology

final topology (plural final topologies)

1. (topology) Given a set ${\displaystyle X}$, a family of topological spaces ${\displaystyle (M_{i},T_{i})_{i\in I}}$ and a family of functions ${\displaystyle f_{i}:M_{i}\to X}$, the final topology is the finest topology on ${\displaystyle X}$ such that all ${\displaystyle f_{i}}$ are continuous.

• quotient topology

• initial topology