Question

Given a metric space Y, a point L in Y, and f:[0,infinity) -> Y, f has...

Given a metric space Y, a point L in Y, and f:[0,infinity) -> Y, f has a limit L element of Y at infinity, written, if for every epsilon greater than 0 there is a C>0 such that if x>C then d(f(x),L) < epsilon. Prove, if f:[0,infinity) -> Y is continuous and has a limit at infinity, 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, 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).
Let f be defined on the (0,infinity). Prove that the limit as x approaches infinity of...
Let f be defined on the (0,infinity). Prove that the limit as x approaches infinity of F(x) =L if and only if the limit as x approaches 0 from the right of f(1/x) = L. Does this hold if we replace L with either infinity or negative infinity?
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.
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 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, 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 metric space, and let U denote the set of all uniformly...
Let (X, d) be a metric space, and let U denote the set of all uniformly continuous functions from X into R. (a) If f,g ∈ U and we define (f + g) : X → R by (f + g)(x) = f(x) + g(x) for all x in X, show that f+g∈U. In words,U is a vector space over R. (b)If f,g∈U and we define (fg) : X → R by (fg)(x) = f(x)g(x) for all x in X,...
Let (X,d) be a metric space. Let E ⊆ X. Consider the set L of all...
Let (X,d) be a metric space. Let E ⊆ X. Consider the set L of all points in X which are limits of sequences contained in E. Prove or disprove the following: (a) L⊆E. (b) L⊆Ē. (c) L̄ ⊆ Ē.
Given a metric space Z and F⊆X⊆Z define F is relatively closed in X. Show, F...
Given a metric space Z and F⊆X⊆Z define F is relatively closed in X. Show, F is relatively closed in X if and only if there is a closed set C⊆Z such that F=C∩X.
Given a metric space Z and F⊆X⊆Z define F is relatively closed in X. Show, F...
Given a metric space Z and F⊆X⊆Z define F is relatively closed in X. Show, F is relatively closed in X if and only if there is a closed set C⊆Z such that F=C∩X.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT