initial topology

initial topology (plural initial 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 ${\displaystyle f_{i}:X\to M_{i}}$, the initial topology is the coarsest topology on ${\displaystyle X}$ such that all ${\displaystyle f_{i}}$ are continuous.

• product topology

• final topology