Question

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.

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, 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
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, 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.
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, 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).
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.
The product of two metric spaces (Y, dY ) and (Z, dZ) is the metric space...
The product of two metric spaces (Y, dY ) and (Z, dZ) is the metric space (Y × Z, dY ×Z), where dY ×Z is defined by dY ×Z((y, z),(y 0 , z0 )) = dY (y, y0 ) + dZ(z, z0 ). Assume that (Y, dY ) and (Z, dZ) are compact. Prove that (Y × Z, dY × dZ) is compact.
suppose X ,Y are T2 spaces ...prove that X x Y are t2 spaces
suppose X ,Y are T2 spaces ...prove that X x Y are t2 spaces
Please explain step by step. 3. (a) Assume X is a separable metric space, Y is...
Please explain step by step. 3. (a) Assume X is a separable metric space, Y is any subspace of X. Prove that Y is also separable. (b) Assume X is a compact metric space. Prove that X is separable
Suppose A is bounded and not compact. Prove that there is a function that is continuous...
Suppose A is bounded and not compact. Prove that there is a function that is continuous on A, but not uniformly continuous. Give an example of a set that is not compact, but every function continuous on that set is uniformly continuous.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT