# Connected/Disconnected all the same to me

1. Dec 16, 2007

### marlen

Connected/Disconnected....all the same to me....

My question for all of you ladies and gentlemen is

what would be considered as an example of a connected set in R squared that becomes disconnected when we remove one point.

My answer would be sin(x/2), but is there a simpler example.

2. Dec 16, 2007

### quasar987

consider two closed balls with just one point in common.

Or like you said, a curve that does close in on itself.

3. Dec 16, 2007

### marlen

Huh? I'm confused.

Would 1/x work? What would be a solid example, one that I could understand?

4. Dec 16, 2007

### marlen

S = f(x; y) : y = 1/x; 0 < x  1g [ f(x; 0) : 1  x  0g would this work

5. Dec 16, 2007

### marlen

TOTALLY DISREGARD THIS COMMENT

6. Dec 16, 2007

### marlen

S = {(x,y): y = 1/x, 0 < x $$\leq$$ 1} $$\cup$$ {(x,0): -1 $$\leq$$ x $$\leq$$ 0}

I meant would this work?

7. Dec 16, 2007

### Dick

No, because S isn't connected. Either part of S would work.

8. Dec 16, 2007

### HallsofIvy

Staff Emeritus
Or A= {(x,y)| y= 0} will do.

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