Question

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.

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
Suppose that f : X  → Y and g: X  → Y are continuous maps between topological spaces...
Suppose that f : X  → Y and g: X  → Y are continuous maps between topological spaces and that Y is Hausdorff. Show that the set A = {x ∈ X : f(x) = g(x)} is closed in X.
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 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
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.
Given two topological spaces with X={d,e,f} and Y = {d, 2,3,8}. Explain why they are not...
Given two topological spaces with X={d,e,f} and Y = {d, 2,3,8}. Explain why they are not homeomorphic.
If X and Y are discrete topological spaces, how do I prove X x Y is...
If X and Y are discrete topological spaces, how do I prove X x Y is also discrete? How would I prove the converse is true, could I ? Very interested. Please explain. Like to please break down into steps that would make sense. Not sure if I have to use facts of product topology and discrete topology and how to use them.
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 (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)
Prove that if f: X → Y is a continuous function and C ⊂ Y is...
Prove that if f: X → Y is a continuous function and C ⊂ Y is closed that the preimage of C, f^-1(C), is closed in X.
Let X be a topological space and A a subset of X. Show that there exists...
Let X be a topological space and A a subset of X. Show that there exists in X a neighbourhood Ox of each point x ∈ A such that A∩Ox is closed in Ox, if and only if A is an intersection of a closed set with an open set.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT