I need some help with understanding this proof. I have 2 questions:
- What are those functions $f$,$g$? I mean what is the idea behind them?
- Why do we consider $f^{-1}(0)$ exactly? Where does this $0$ come from?
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You have to look back at the definition of transverse and regular to find out where $f$ and $g$ come from. That's more than we can provide here. – Ethan Bolker Jan 10 '24 at 12:38
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1this f and g cames from the relugar value theorem, see: https://math.stackexchange.com/questions/913616/regular-value-theorem-using-implicit-function-theorem-in-calculus – Gabriel Palau Jan 10 '24 at 12:43
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1Do you know the regular value/preimage theorem, if not look it up. It is used here as the approach. – tychonovs-scholar Jan 10 '24 at 12:46
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Thank you for replying. But I still don't understand why we consider exactly $0$ here and not any other value. – bobby shmurda Jan 10 '24 at 13:33