Topologist Sine Curve

Asked Oct 30 '13 at 05:30

Active Oct 30 '13 at 05:30

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I am trying to prove that the topologist sine curve is not path connected. I think I have a proof but my proof relies on Intermediate Value Theorem. So, I was wondering if there is a way to prove it without using Intermediate Value Theorem.

Thank You.

asked Oct 30 '13 at 05:30

user20694

A google search turns up this http://math.stanford.edu/~conrad/diffgeomPage/handouts/sinecurve.pdf – TBrendle Oct 30 '13 at 05:39
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What's wrong with using the intermediate value theorem? – Daniel McLaury Oct 30 '13 at 05:44
@DanielMcLaury I am in a topology class. Most of us know about the intermediate value theorem but we have not covered it in class yet. – user20694 Oct 30 '13 at 05:48
Do you know how to prove the intermediate value theorem? – Daniel McLaury Oct 30 '13 at 05:48
@DanielMcLaury Yes I do. I suppose you are suggesting that I should prove the intermediate value theorem as part of the entire proof. – user20694 Oct 30 '13 at 05:57
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The intermediate value theorem is just a special case of the fact that a continuous image of a connected set is connected; have you proved that more general result? – Brian M. Scott Nov 02 '13 at 03:46

Topologist Sine Curve

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