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beetle2
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Let [itex](X; T ) [/itex] be a topological space. Given the set Y and the function [itex]f : X \rightarrow Y [/itex], define
[itex]U := {H\inY \mid f^{-1}(H)\in T}[/itex]
Show that U is the finest topology on Y with respect to which f is continuous.
I was wondering is this implying that [itex]U[/itex] is the Quotient topology?
[itex]U := {H\inY \mid f^{-1}(H)\in T}[/itex]
Show that U is the finest topology on Y with respect to which f is continuous.
Homework Equations
The Attempt at a Solution
I was wondering is this implying that [itex]U[/itex] is the Quotient topology?