help, it's urgent

From: Tern (ternnret_at_yahoo.it)
Date: 10/23/04 

Date: 23 Oct 2004 08:42:53 -0700

My problem is this

Let C^infty_W(U, R^n) denotes the space of
C^infty maps g from U to R^n with the Weak topology.
Let's pi: R^n --> R^a denotes the projection,
and pi o g the product of composition of such maps g and pi.

My book says:
Fixed a map g in C^infty_W(U, R^n),
by Morse-Sard theorem applied to
pi o g: U --> R^n/R^a
there exists a sequence {y_k}_k in R^n
tending to 0 such that
forall k in N, pi(y_k) in R^n/R^a
is a regular value of pi o g.

My ask is:
I know that by Morse-Sard theorem the set of regular value
of pi o g is dense in R^n/R^a. Then it's reasonable thet there exists
a sequence {y_k}_k in R^n such that forall k in N, pi(y_k) in R^n/R^a
is a regular value of pi o g.
But, for what reason should exist such a sequence tending to 0 ??

Thanks for all
Tern

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