Hello,

since I don't want to write down a whole page of the book, you need to have the book to answer me. I'm aware of that and I hope someone has it.

On page 8 Milnor shows that #$\displaystyle f^{-1}(y) $ is locally constant as a function of y.

That means, that for every regular value y, there exists a neighborhood V of y in N,so that every x in V is a regular value(did i get this right?) and #$\displaystyle f^{-1}(y) $=#$\displaystyle f^{-1}(y') $ for every y' in V.

In the last line of the section, he shows a possible neighborhood V of y:

$\displaystyle $V=V_1 \cap ... \cap V_k - f(M-U_1-...-U_k)$$

I see that $\displaystyle V_1 \cap ... \cap V_k$ is a neigborhood of y, but why is it still one, if you remove $\displaystyle $f(M-U_1-...-U_k)$$?

Thanks in advance,

engmaths