final topology

Noun

Meaning

final topology (plural final 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


:

M

i


→
X


{\displaystyle f_{i}:M_{i}\to X}

, the final topology is the finest topology on



X


{\displaystyle X}

such that all




f

i




{\displaystyle f_{i}}

are continuous.

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