Balls connected in R^n

**Andreamet** · Apr 8th 2009, 03:51 PM

Show that the open balls and closed balls in the standard metric on $\mathbb{R}^n$ are connected in $\mathbb{R}^n$

**Jhevon** · Apr 8th 2009, 04:18 PM

Originally Posted by Andreamet

Show that the open balls and closed balls in the standard metric on $\mathbb{R}^n$ are connected in $\mathbb{R}^n$

note that $S \subseteq \mathbb{R}^n$ is path-wise connected, implies that it is connected. thus, you have the desired result, if you can show that open balls and closed balls are path-wise connected.

note that any two points in an open or closed ball can be connected by a straight line that is contained in the ball

Thread: Balls connected in R^n

LinkBack

Thread Tools

Display

Balls connected in R^n

Similar Math Help Forum Discussions

Can open balls and pairwise intersections of balls generate a topology?

Every path-connected metric space is connected

a basket contains 5 red balls, 3 blue balls, 1 green balls

Proof that union of two connected non disjoint sets is connected

proving that a subset of reals is connected if and only if path-connected

Search Tags