1.NounGiven a set
X
{\displaystyle X}
, a family of topological spaces
(
M
i
,
T
i
)
i
∈
I
{\displaystyle (M_{i},T_{i})_{i\in I}}
and a family of functions
f
i
:
X
→
M
i
{\displaystyle f_{i}:X\to M_{i}}
, the initial topology is the coarsest topology on
X
{\displaystyle X}
such that all
f
i
{\displaystyle f_{i}}
are continuous.