Question

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)

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

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 P = (x1, d1) -> (x2, d2) and Q = (x2, d2) -> (x3, d3)....
Let P = (x1, d1) -> (x2, d2) and Q = (x2, d2) -> (x3, d3). P and Q are covering maps. Show that the composition of P and Q (P ◦ Q) is also a covering map from (x1, d1) to (x3, d3). Thank you!
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
Two metric spaces (X,dx) and (Y,dY) are said to be bi-Lipshitz equivalent if there exists a...
Two metric spaces (X,dx) and (Y,dY) are said to be bi-Lipshitz equivalent if there exists a surjective function f: X -> Y and a number K >= 1 such that for all x1,x2 in X it the case (1/K)dx(x1,x2)<=dY(f(x1),f(x2))<=Kdx(x1,x2) Prove the function f of the definition of bi-Lipschitz equivalence is a bijection. (Geometric group theory)
Assume that (X, dX) and (Y, dY ) are complete spaces, and give X × Y...
Assume that (X, dX) and (Y, dY ) are complete spaces, and give X × Y the metric d defined by d((x1, y1),(x2, y2)) = dX(x1, x2) + dY (y1, y2) Show that (X × Y, d) is complete.
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.
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 f:A->B and let D1, D2, and D be subsets of A. Prove or Disprove F^-1(D1UD2)=F^-1(D1)UF^-1(D2)
let f:A->B and let D1, D2, and D be subsets of A. Prove or Disprove F^-1(D1UD2)=F^-1(D1)UF^-1(D2)
Let F (x1, x2) = ln(1 + 4x1 + 7x2 + 6x1x2), x = (x1, x2)...
Let F (x1, x2) = ln(1 + 4x1 + 7x2 + 6x1x2), x = (x1, x2) ∈ R . →− (a) Find the linearization of F at 0 . Show F is continuously differentiable, that is, C , at 0 .