Question

Suppose that X is complete. Show that a subset Y of X is complete if Y...

Suppose that X is complete. Show that a subset Y of X is complete if Y is closed

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

Homework Answers

Answer #1

Please feel free to ask any query in the comment box and don't forget to rate if you like.

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
Show that a subset Y of X is closed if Y is complete.
Show that a subset Y of X is closed if Y is complete.
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...
Let Y be a subspace of X and let S be a subset of Y. Show...
Let Y be a subspace of X and let S be a subset of Y. Show that the closure of S in Y coincides with the intersection between Y and the closure of S in X.
Recall that a subset A (of N, Z, Q) is called downward closed when x ∈...
Recall that a subset A (of N, Z, Q) is called downward closed when x ∈ A and y < x implies y ∈ A. Suppose that A is a downward closed subset of Z, and consider the subsets B = {x + 1 ∈ Z | (∃y ∈ A).x2 ≤ y} C = {x − 1 ∈ Z | (∃y ∈ A).x < y2 } For each of B, C, determine whether it is downward closed in Z. Explain...
Suppose that E is a closed connected infinite subset of a metric space X. Prove that...
Suppose that E is a closed connected infinite subset of a metric space X. Prove that E is a perfect set.
Let X be a subset of the integers from 1 to 1997 such that |X|≥34. Show...
Let X be a subset of the integers from 1 to 1997 such that |X|≥34. Show that there exists distinct a,b,c∈X and distinct x,y,z∈X such that a+b+c=x+y+z and {a,b,c}≠{x,y,z}.
Let (X,d) be a metric space which contains an infinite countable set Ewith the property x,y...
Let (X,d) be a metric space which contains an infinite countable set Ewith the property x,y ∈ E ⇒ d(x,y) = 1. (a) Show E is a closed and bounded subset of X. (b) Show E is not compact. (c) Explain why E cannot be a subset of Rn for any n.
Determine if the subset W={[x y]∈R2∣ x+y ≥0} is a subspace of R2.
Determine if the subset W={[x y]∈R2∣ x+y ≥0} is a subspace of R2.
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.
Problem 6. For a closed convex nonempty subset K of a Hilbert space H and x...
Problem 6. For a closed convex nonempty subset K of a Hilbert space H and x ∈ H, denote by P x ∈ K a unique closest point to x among points in K, i.e. P x ∈ K such that ||P x − x|| ≤ ||y − x||, for all y ∈ K. First show that such point P x exists and unique. Next prove that all x, y ∈ H ||P x − P y|| ≤ ||x −...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT