Question

If A and B are closed subsets of a metric space X, whose union and intersection...

If A and B are closed subsets of a metric space X, whose union and intersection are connected, show that A and B themselves are connected. Give an example showing that the assumption of closedness is essential.

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 X and Y are connected subsets of metric space X, the X intersection Y is...
Suppose X and Y are connected subsets of metric space X, the X intersection Y is not empty. show Y union X is connected.
Let E and F be two disjoint closed subsets in metric space (X,d). Prove that there...
Let E and F be two disjoint closed subsets in metric space (X,d). Prove that there exist two disjoint open subsets U and V in (X,d) such that U⊃E and V⊃F
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.
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.
Prove that the Gromov-Hausdorff distance between subsets X and Y of some metric space Z is...
Prove that the Gromov-Hausdorff distance between subsets X and Y of some metric space Z is 0 if and only if X = Y question related to Topological data analysis 2
Show that an intersection of finitely many open subsets of X is open.
Show that an intersection of finitely many open subsets of X is open.
10. Prove if X and Y are nonempty closed subsets of [a,b]⊂ ℝ such that X∪Y=[a,b],...
10. Prove if X and Y are nonempty closed subsets of [a,b]⊂ ℝ such that X∪Y=[a,b], then X∩Y≠ ∅.
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.
is about metric spaces: Let X be a metric discret space show that a sequence x_n...
is about metric spaces: Let X be a metric discret space show that a sequence x_n in X converge to l in X iff x_n is constant exept for a finite number of points.