Hii(adsbygoogle = window.adsbygoogle || []).push({});

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 ...

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Some a questions in Metric Spaces

**Physics Forums | Science Articles, Homework Help, Discussion**