Question

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.

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 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.
Let X be a topological space with topology T = P(X). Prove that X is finite...
Let X be a topological space with topology T = P(X). Prove that X is finite if and only if X is compact. (Note: You may assume you proved that if ∣X∣ = n, then ∣P(X)∣ = 2 n in homework 2, problem 2 and simply reference this. Hint: Ô⇒ follows from the fact that if X is finite, T is also finite (why?). Therefore every open cover is already finite. For the reverse direction, consider the contrapositive. Suppose X...
Prove that a disjoint union of any finite set and any countably infinite set is countably...
Prove that a disjoint union of any finite set and any countably infinite set is countably infinite. Proof: Suppose A is any finite set, B is any countably infinite set, and A and B are disjoint. By definition of disjoint, A ∩ B = ∅ Then h is one-to-one because f and g are one-to one and A ∩ B = 0. Further, h is onto because f and g are onto and given any element x in A ∪...
Prove that a subset of a countably infinite set is finite or countably infinite.
Prove that a subset of a countably infinite set is finite or countably infinite.
(i)LetX be a set andT,T′ two toplogies onX withT ⊂T′. What does connectedness of X in...
(i)LetX be a set andT,T′ two toplogies onX withT ⊂T′. What does connectedness of X in one topology imply about connectedness in the other? 2 (ii) Let X be an infinite set. Show that X is connected in the cofinite topology. (iii) Let X be an infinite set with the cocountable topology. What can you say about the connectedness of X?
Let the set N of natural numbers be endowed with the cofinite topology (in which a...
Let the set N of natural numbers be endowed with the cofinite topology (in which a set is open if and only if it is empty or its complement is finite). (a) Is N connected? Justify your answer. (b) Is N compact? Justify your answer. (c) Explain why the function f : N → N, n→ n ^3 is continuous. (d) Exhibit a function g : N → N which is not continuous.
1. Suppose that ? is a finite dimensional vector space over R. Show that if ???(?...
1. Suppose that ? is a finite dimensional vector space over R. Show that if ???(? ) is odd, then every ? ∈ L(? ) has an eigenvalue. (Hint: use induction). (please provide a detailed proof) 2. Suppose that ? is a finite dimensional vector space over R and ? ∈ L(? ) has no eigenvalues. Prove that every ? -invariant subspace of ? has even dimension.
1.- Is it possible that two topologies τ1, τ2 in X generate the same relative topology...
1.- Is it possible that two topologies τ1, τ2 in X generate the same relative topology in a subset A ⊂ X? 2.- Characterize all compact subspaces of (R, τe). (τe is subspace topology)
If a, b ∈ R with a not equal to 0, show that the infinite set...
If a, b ∈ R with a not equal to 0, show that the infinite set {1,(ax + b),(ax + b)2 ,(ax + b)3 , · · · } of polynomials is a basis for F[x].
(a) This exercise will give an example of a connected space which is not locally connected....
(a) This exercise will give an example of a connected space which is not locally connected. In the plane R2 , let X0 = [0, 1] × {0}, Y0 = {0} × [0, 1], and for each n ∈ N, let Yn = {1/n} × [0,1]. Let Y = X0 ∪ (S∞ n=0 Yn). as a subspace of R 2 with its usual topology. Prove that Y is connected but not locally connected. (Note that this example also shows that...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT