- Thread starter
- #1

- Mar 10, 2012

- 835

Hello MHB,

I have the following conjecture which I cannot seem to settle either way:

Let $f:[0,1]\to\mathbb R^2$ be a differentiable function such that $f(0)=(0,0)$.

Then there exists a continuous function $g:[0,1]\to\mathbb R^2$ such that:

1) $g(0)=(0,0)$

2) $g([0,1])\cap f([0,1])=\{(0,0)\}$.

3) $g$ is not a constant function. (Forgot to add this earlier.)

Basically what I am trying to prove is that if we have a differentiable curve in $\mathbb R^2$ whic passes through origin then we can find a continuous curve in $\mathbb R^2$ which intersects the gives curve only at origin.

I have the following conjecture which I cannot seem to settle either way:

Let $f:[0,1]\to\mathbb R^2$ be a differentiable function such that $f(0)=(0,0)$.

Then there exists a continuous function $g:[0,1]\to\mathbb R^2$ such that:

1) $g(0)=(0,0)$

2) $g([0,1])\cap f([0,1])=\{(0,0)\}$.

3) $g$ is not a constant function. (Forgot to add this earlier.)

Basically what I am trying to prove is that if we have a differentiable curve in $\mathbb R^2$ whic passes through origin then we can find a continuous curve in $\mathbb R^2$ which intersects the gives curve only at origin.

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