Question

Show that if Y is G-delta set in X , and if X is a compact...

Show that if Y is G-delta set in X , and if X is a compact Hausdorff space, then Y is a Baire space in subspace topology.

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
Show that if X is an infinite set, then it is connected in the finite complement...
Show that if X is an infinite set, then it is connected in the finite complement topology. Show that in the finite complement on R every subspace is compact.
(a) If G is an open set and K is a compact set with K ⊆...
(a) If G is an open set and K is a compact set with K ⊆ G, show that there exists a δ > 0 such that {x|dist(x, K) < δ} ⊆ G. (b) Find an example of an open subset G in a metric space X and a closed, non compact subset F of G such that there is no δ > 0 with {x|dist(x, F) < δ} ⊆ G
Show that a compact subset of a Hausdorff space is closed in detail.
Show that a compact subset of a Hausdorff space is closed in detail.
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...
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.
1. Consider the set U={(x,y) in R2| -1<x<1 and y=0}. Is U open in R2? Is...
1. Consider the set U={(x,y) in R2| -1<x<1 and y=0}. Is U open in R2? Is it open in R1? Is it open as a subspace of the disk D={(x,y) in R2 | x^2+y^2<1} ? 2. Is there any subset of the plane in which a single point set is open in the subspace topology?
Exercise 9.1.11 Consider the set of all vectors in R2,(x, y) such that x + y...
Exercise 9.1.11 Consider the set of all vectors in R2,(x, y) such that x + y ≥ 0. Let the vector space operations be the usual ones. Is this a vector space? Is it a subspace of R2? Exercise 9.1.12 Consider the vectors in R2,(x, y) such that xy = 0. Is this a subspace of R2? Is it a vector space? The addition and scalar multiplication are the usual operations.
Suppose G acts on a set X, and x,y ∈ X. Show that either O(x) =...
Suppose G acts on a set X, and x,y ∈ X. Show that either O(x) = O(y) or O(x) ∩ O(y) = ∅.
Is the set of all x, y, z such x+ 3y + 2z = 0 a...
Is the set of all x, y, z such x+ 3y + 2z = 0 a subspace of R^3 ? If so find a basis for the space.
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.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT