initial topology

Noun

Meaning

initial topology (plural initial topologies)

(topology) Given 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.

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