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- #1

- Jun 22, 2012

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I am focused on Chapter 3: Metrics and Norms ... ...

I need help Exercise 32 on page 46 ... ...

Exercise 32 reads as follows:

I have not been able to make much progress ...

We have ...

\(\displaystyle B_r(x) = \{ y \in M \ : \ d(x, y) \lt r \}\)

... and ...

\(\displaystyle B_r(0) = \{ y \in M \ : \ d(0, y) \lt r \}\)

... and ...

\(\displaystyle x + B_r(0) = x + \{ y \in M \ : \ d(0, y) \lt r \}\)

But ... how do we formally proceed from here ...

Hope that someone can help ...

Peter

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The above post refers to/involves the notion of an open ball ... so I am providing Carothers' definition of the same ... as follows:

The above post also refers to/involves the notion of a normed vector space ... so I am providing Carothers' definition of the same ... as follows:

Hope that helps ...

Peter