Let [itex](X; T ) [/itex] be a topological space. Given the set Y and the function [itex]f : X \rightarrow Y [/itex], define(adsbygoogle = window.adsbygoogle || []).push({});

[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.

2. Relevant equations

3. The attempt at a solution

I was wondering is this implying that [itex]U[/itex] is the Quotient topology?

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Continuous topology problem

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