Transversality as an extension of the notion of regularity p.28 in Guillemin & Pollack.

Question

The book "Differential Topology" book is explaining this in the image below:

But I do not understand:

In the first paragraph:

The 2 statements starting from the fifth line, could anyone explain them for me please?

In the last paragraph:

I could not understand the statements starting from the second line till the end of the paragraph, Could anyone explain this for me please?

Answer 1

I think the author is assuming you've done p.25 problem 4. I think once you understand this, you'll better understand the sentences after it. One important thing to keep in mind (and a general theme of this book) is that not all of these expositions are iron-clad proofs. In my opinion, you should try as best as possible to rewrite the arguments laid out in rigor. Also, for the last paragraph, see the proposition at the bottom of page 24.

I hope this helps.