Question

Let X, Y be metric spaces, with Y complete. Let S ⊂ X and let f...

Let X, Y be metric spaces, with Y complete. Let S ⊂ X and let f : S → Y be uniformly continuous. (a) Suppose p ∈ S closure and (pn) is a sequence in S with pn → p. Show that (f(pn)) converges in y to some point yp.

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Let X and Y be metric spaces. Let f be a continuous function from X onto...
Let X and Y be metric spaces. Let f be a continuous function from X onto Y, that is the image of f is equal to Y. Show that if X is compact, then Y is compact
Let (X, dX) and (Y, dY ) be metric spaces and let f : X →...
Let (X, dX) and (Y, dY ) be metric spaces and let f : X → Y be a continuous bijection. Prove that if (X, dX) is compact, then f is a homeomorphism
Please prove the following theorem: Suppose (X,p) and (Y,b) are metric spaces, X is compact, and...
Please prove the following theorem: Suppose (X,p) and (Y,b) are metric spaces, X is compact, and f:X→Y is continuous. Then f is uniformly continuous.
Let (X1,d1) and (X2,d2) be metric spaces, and let y∈X2. Define f:X1→X2 by f(x) =y for...
Let (X1,d1) and (X2,d2) be metric spaces, and let y∈X2. Define f:X1→X2 by f(x) =y for all x∈X1. Show that f is continuous. (TOPOLOGY)
Suppose d and d 0 are both metrics on X and that the metric spaces (X,...
Suppose d and d 0 are both metrics on X and that the metric spaces (X, d) and (X, d0 ) have the same open sets. Show, the sequence (an) from X converges in (X, d) if and only if it converges in (X, d0 ) and then to the same limit.
is about metric spaces: Let X be a metric discret space show that a sequence x_n...
is about metric spaces: Let X be a metric discret space show that a sequence x_n in X converge to l in X iff x_n is constant exept for a finite number of points.
Suppose K is a nonempty compact subset of a metric space X and x∈X. Show, there...
Suppose K is a nonempty compact subset of a metric space X and x∈X. Show, there is a nearest point p∈K to x; that is, there is a point p∈K such that, for all other q∈K, d(p,x)≤d(q,x). [Suggestion: As a start, let S={d(x,y):y∈K} and show there is a sequence (qn) from K such that the numerical sequence (d(x,qn)) converges to inf(S).] Let X=R^2 and T={(x,y):x^2+y^2=1}. Show, there is a point z∈X and distinct points a,b∈T that are nearest points to...
If X, Y are topological spaces and f : X → Y we call the graph...
If X, Y are topological spaces and f : X → Y we call the graph of f the set Γf = {(x, f(x)); x ∈ X} which is a subset of X × Y. If X and Y are metric spaces and f is a continuous function prove that the graph of f is a closed set.
Let (X, d) be a compact metric space and let A ⊆ X. Suppose that A...
Let (X, d) be a compact metric space and let A ⊆ X. Suppose that A is not compact. Prove that there exists a continuous function f : A → R, from (A, d) to (R, d|·|), which is not uniformly continuous.
Let (X, d) be a compact metric space and F: X--> X be a function such...
Let (X, d) be a compact metric space and F: X--> X be a function such that d(F(x), F(y)) < d(x, y). Let G: X --> R be a function such that G(x) = d(F(x), x). Prove G is continuous (assume that it is proved that F is continuous).
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT