1. ## continuous

if f : X--> Y is continuous and onto such that X is compact.

let g:Y--> Z is a function such that g0f is continuous. prove that g is contiuous.

how it can be prceeded.

2. ## Re: continuous

Is there an assumption over $X$ like Hausdorff? You can show that $g^{-1}(F)$ is closed for $F$ closed.