Questions concerning path-connectedness of Epsilon-Ball

[brickcitie]

Homework Statement

I'm asked to show that an epsilon-disc in R^n is path-connected.

Homework Equations

The Attempt at a Solution

I can kind of understand in my head why it must be, but I literally have no clue how to begin a rigorous attempt at this. I know I need to define a continuous function over [a,b] with f(a) = x and f(b) = y for any two points x,y in the epsilon-disc, but I am not sure how to define this function. Any help would be much appreciated.

 

[Dick]

Homework Statement

I'm asked to show that an epsilon-disc in R^n is path-connected.

Homework Equations

The Attempt at a Solution

I can kind of understand in my head why it must be, but I literally have no clue how to begin a rigorous attempt at this. I know I need to define a continuous function over [a,b] with f(a) = x and f(b) = y for any two points x,y in the epsilon-disc, but I am not sure how to define this function. Any help would be much appreciated.

What you need to show is that there is a path connecting any two points in a ball. Define a path explicitly. Go through the center if that makes it easier.