Question

Prove that if X is a connected Hausdorff space and X has more than one point,...

Prove that if X is a connected Hausdorff space and X has more than one point, then
X is infinite.

Please show all work and write clear

I am stupid

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
Prove that if a topological space X has the fixed point property, then X is connected
Prove that if a topological space X has the fixed point property, then X is connected
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.
A tree is a connected graph that contains no cycles. Prove that any tree with two...
A tree is a connected graph that contains no cycles. Prove that any tree with two or more vertices has chromatic number 2. Hi there! Please WRITE LEGIBLY and with clear steps. A lot of times I get confused by the solutions. Thank you!
1.- Prove the intermediate value theorem: let (X, τ) be a connected topological space, f: X...
1.- Prove the intermediate value theorem: let (X, τ) be a connected topological space, f: X - → Y a continuous transformation and x1, x2 ∈ X with a1 = f (x1), a2 = f (x2) ( a1 different a2). Then for all c∈ (a1, a2) there is x∈ such that f (x) = c. 2.- Let f: X - → Y be a continuous and suprajective transformation. Show that if X is connected, then Y too.
Let A⊆(X,d) a metric space. Suppose there are an infinite number of elements in e1,e2,e3,...∈ A...
Let A⊆(X,d) a metric space. Suppose there are an infinite number of elements in e1,e2,e3,...∈ A such that d(ei,ej)=4 if i≠j and d(ei,ej)=0 if i=j for i,j=1,2,3... Prove that A is not totally bounded. (Please do not write in script and show all your steps and definitions used)
(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...
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...
Using a step by step proof format Please prove: Given that x is a vector in...
Using a step by step proof format Please prove: Given that x is a vector in the span of V, where V is a linearly independent set of vectors, show that there is ONLY ONE linear combination of the vectors in V that yields x. (Hint: to show that something is unique, assume that there is more than one such thing and show that this leads to a contradiction)
Prove that there exist n consecutive positive integers each having a (nontrivial) square factor. How would...
Prove that there exist n consecutive positive integers each having a (nontrivial) square factor. How would you then modify your proof so that each of these integers instead has a cube factor (or more generally, a kth power factor where k ≥ 2)? This is a number theory question. Please show all steps and make clear notes about what is happening for a clear understanding. Please write clearly or do in latex. Thank you
Given a metric space Y, a point L in Y, and f:[0,infinity) -> Y, f has...
Given a metric space Y, a point L in Y, and f:[0,infinity) -> Y, f has a limit L element of Y at infinity, written, if for every epsilon greater than 0 there is a C>0 such that if x>C then d(f(x),L) < epsilon. Prove, if f:[0,infinity) -> Y is continuous and has a limit at infinity, then f is uniformly continuous.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT