Re: help with math translation from French

In article <1183196056.612254.72190@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>, gius
<giu.giorgi@xxxxxxxxx> wrote:

Dear all,

I ask you to translate the following paper of mathematics (it
consists in four lines) form French to English, please.


http://i7.tinypic.com/4uyknyu.jpg


I beg you to help me, it's very important for me.


Best regards, Thank you in advance,
Giusy


V_n is an open set of M_{n+1}. The restriction of phi_n to V_n
is an embedding (immersion?) of an open set of M_{n+1} in E.
One applies this map to an embedding of M_{n+1} in E.
By applying the theorem of isotopy of a tubular neighborhood:
one applies the embedding to an embedding of a tubular neighborhood
of M_{n+1} in E of the sort in the following commutative
diagram:

I'm a little unsure about how to translate "plongement"
and "\'etand"---probably you need a topologist for that...

--
G. A. Edgar http://www.math.ohio-state.edu/~edgar/
.

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