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Topology of open set(newbie, I am stuck help!)
1. The problem statement, all variables and given/known data
Hi just found this found and have some basic questions about topology.
If let say exist a metrix space (M,s) and two points [tex]x \neq y[/tex] in M. Then show that there exists open sets [tex]V_1,V_2 \in \mathcal{T}_s[/tex] such that [tex]x \in V_1[/tex] and [tex]x \in V_2[/tex] and finally [tex]V_1 \cap V_2 = \emptyset[/tex]
2. Relevant equations
3. The attempt at a solution
I try to solve question 1)
For V_1 to be an open set set then there must exist an open ball such that B(x)_r < r where is the radius of the ball which is M. Have I understood this correctly?
1. The problem statement, all variables and given/known data
Hi just found this found and have some basic questions about topology.
If let say exist a metrix space (M,s) and two points [tex]x \neq y[/tex] in M. Then show that there exists open sets [tex]V_1,V_2 \in \mathcal{T}_s[/tex] such that [tex]x \in V_1[/tex] and [tex]x \in V_2[/tex] and finally [tex]V_1 \cap V_2 = \emptyset[/tex]
2. Relevant equations
3. The attempt at a solution
I try to solve question 1)
For V_1 to be an open set set then there must exist an open ball such that B(x)_r < r where is the radius of the ball which is M. Have I understood this correctly?
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