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## Main Question or Discussion Point

Hii

my Dears....

I'm new student in the Math & I'm so bad in the English Language..

But, I want to learn this language ...

to excuse me ...

I have some a questions about Metric Spaces ..

Q1:If (X,d) is a metric spaces . Prove the fallwing:

1* ld(x,y)-d(z,y)l [tex]\leq[/tex] d(x,y)+d(y,w).

2* ld(x,z)-d(y,z)l [tex]\leq[/tex] d(x,y). ..??

Q2:Prove that:

Xn ـــــــــ> X iff [tex]\forall[/tex] V (neighborhood of X) [tex]\exists[/tex] n0 is number s.t Xn[tex]\in[/tex]V [tex]\forall[/tex]n>n0....??

Q3: If (X1,d1) & (X2,d2) is a metrics spaces, Prove that X=X1xX2 () is a metric spaces whith a metric defind by: d(x,y)=d1(x1,y1)+d2(x2,y2) s.t x1,y1[tex]\in[/tex]X1..??

Q4:Prove that every Cauchy sequence in a metric space (X, d) is bounded...??

I need to help by speed..

Thanx ...

my Dears....

I'm new student in the Math & I'm so bad in the English Language..

But, I want to learn this language ...

to excuse me ...

I have some a questions about Metric Spaces ..

Q1:If (X,d) is a metric spaces . Prove the fallwing:

1* ld(x,y)-d(z,y)l [tex]\leq[/tex] d(x,y)+d(y,w).

2* ld(x,z)-d(y,z)l [tex]\leq[/tex] d(x,y). ..??

Q2:Prove that:

Xn ـــــــــ> X iff [tex]\forall[/tex] V (neighborhood of X) [tex]\exists[/tex] n0 is number s.t Xn[tex]\in[/tex]V [tex]\forall[/tex]n>n0....??

Q3: If (X1,d1) & (X2,d2) is a metrics spaces, Prove that X=X1xX2 () is a metric spaces whith a metric defind by: d(x,y)=d1(x1,y1)+d2(x2,y2) s.t x1,y1[tex]\in[/tex]X1..??

Q4:Prove that every Cauchy sequence in a metric space (X, d) is bounded...??

I need to help by speed..

Thanx ...

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