# Open balls and limit points

1. Nov 11, 2011

### srfriggen

While learning about limit points the use of an open ball has been of high discussion. Why can you not use a closed ball to define a limit point?

If someone could give me some intuition as to why I think I may get it.

Thanks.

2. Nov 11, 2011

### micromass

Staff Emeritus
Are you working in metric space?? In that case, you can define limit points using open balls.

Just define x to be a limit point of A if every ball around x intersects A\{x}.

3. Nov 11, 2011

### srfriggen

yes, I am working in a metric space.

So can you use your definition for open and closed balls?

4. Nov 11, 2011

### micromass

Staff Emeritus
No, only for open balls. Think about what could go wrong for closed balls.

5. Nov 11, 2011

### srfriggen

I've been trying to but I can't think of an example where having boundaries on the ball would cause a problem. That's really why I asked the original question.

Can you give me one?

6. Nov 11, 2011

### micromass

Staff Emeritus
What if the ball has radius 0?

7. Nov 11, 2011

### srfriggen

got it, thanks!