- Thread starter
- #1

- Thread starter ianchenmu
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- Thread starter
- #1

- Jan 29, 2012

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Even more, $E$ is pathwise connected. If $x$ and $y$ are in $E$ then, the line segment $x+t(y-x): t \in [0,1]$ is a subset of $E$, so $\gamma:[0,1]\to E,\; \gamma (t)=x+t(y-x)$ is continuous path and connects $x$ to $y$.A set $E⊂\mathbb{R}^{n}$ is convex if, given any two points $x$,$y$$∈E$, the line segment {$x + t(y-x)$ s.t. $t∈[0,1]$}

is contained in $E$. Prove that if $E$ is convex, then $ E$ is connected.