Thank your answer,
I thought I had got it now :frown: So my thought in the previous post about how to show that V1 and V2 are open is that completely wrong?
Hi all here is my trying to ansvar why
V_1 is an open set of M and contains x.
Let x' be a point in the ball B(x,r) and let s = ||x'-x||. We claim that the ball B(x'; r-s) is inside the ball B(x,r), if yes then its open. Then by taking the triangle inequality for any x in
B(x'; r-s)...
Okay I will try to go on from there.
what about question 3? I am told that I have use the fact
d(x,z) \ leq d(x,y) + d(y,z) and then show there does not exist a z which satisfies the above property of the metric and hence the intersection og V1 and V2 are the empty set. How does that sound?
Topology of open set(newbie, I am stuck help!)
Homework Statement
Hi just found this found and have some basic questions about topology.
If let say exist a metrix space (M,s) and two points x \neq y in M. Then show that there exists open sets V_1,V_2 \in \mathcal{T}_s such that x \in...