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Metric spaces

  • #1

Homework Statement



i am required to prove whether the following statement is true or false,

Homework Equations



there exists a metric space (X,d) with B1 contained in B2 contained in
X such that B1=Bo(x1,3), B2=Bo(x2,2), and B2-B1 not equal to the empty set

here Bo denotes the open ball

The Attempt at a Solution



any hints on how to set about this problem?
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
26,258
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Ok, so your space has to contain at least 3 points, right? x1, x2 and some x in B2-B1. Can you define a metric on those three points that doesn't break any rules (like triangle inequality) and satisfies all of the relations?
 

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