1. ## [Topology] Connected Spaces

I realy need some help in the following questions:

1. Let $X$ be a topological space and let A be subgroup of X that contains one and only point from each connected component of X. Prove that $X/A$ is connected.

2. Let $X=R-{0}$ be a subspace of R. Prove that for each n=1,2,3,4... - $X^n$ is locally connected but $X^N$ is not locally connected...

Thanks a lot !

2. Originally Posted by WannaBe
I realy need some help in the following questions:

1. Let $X$ be a topological space and let A be subgroup of X that contains one and only point from each connected component of X. Prove that $X/A$ is connected.

2. Let $X=R-{0}$ be a subspace of R. Prove that for each n=1,2,3,4... - $X^n$ is locally connected but $X^N$ is not locally connected...

Thanks a lot !
What have you done? For one, did you mean subspace or actually subgroup?

3. I meant subspace ofcourse... Sry for the mistake...
I actually have no idea how to start thinking of these two questions... I hope you will be able to give me some hints that will give me a small push here...

Thanks