Hi, everyone:(adsbygoogle = window.adsbygoogle || []).push({});

I have been reading Boothby's intro to diff. manifolds, and in def. 4.3,

talking about 1-1 immersions F:N->M , n and m-mfld. and M an m-mfld.

That:

"...F establishes a 1-1 correspondence between N and the image N'=F(N)

of M. If we use this correspondence to give N' a topology and a C^oo

structure, then N' will be called a submanifold, and F:N->N' a diffeomorphism".

I am just wondering how this topology and C^oo structure are defined.

I imagine we are using pullbacks here, tho, since F is not necessarily

a diffeom. , we cannot pullback by F, except maybe locally, using

the inverse fn. theorem.

And, re the topology on F'(N) , we cannot use subspace, since

F may not be an embedding. Maybe we are using quotient topology,

but it does not seem clear.

Anyone know how the topology and C^oo structure are defined

in N'=F(N)?

I would appreciate any help.

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# Smooth Charts on immersion image.

Can you offer guidance or do you also need help?

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