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- #1

- Jun 22, 2012

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I am focused on Chapter 3: Limits and Continuity ... ...

I need help in order to fully understand Example 3.10 (b) on page 95 ... ...

Example 3.10 (b) reads as follows:

My question is as follows:

Stromberg says that if \(\displaystyle X\) is any set and \(\displaystyle \mathscr{T}\) is the family of all subsets of \(\displaystyle X\) ...

... then \(\displaystyle \mathscr{T}\) is nothing but the metric topology obtained from the discrete metric ...

Can someone demonstrate/explain exactly how/why this is true ...?

Help will be much appreciated ...

Peter

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Example 3.10 (b) above refers to Example 3.2 (a) ... ... so I am providing access to the same ... as follows:

It may help readers of the above post to have access to Stromberg's definition of a topological space ... so I am providing access to the same ... as follows:

Stromberg's definition of a topological space refers to Theorem 3.6 ... ... so I am providing access to the statement of the same ... as follows:

Stromberg's definition of a topological space also refers to Definition 3.3 ... ... so I am providing access to the same ... as follows:

Hope that helps ...

Peter