(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I'm stuck on how to start this. The Hammin metric is define:

http://s1038.photobucket.com/albums/a467/kanye_brown/?action=view¤t=hamming_metric.jpg

and I'm asked to:

http://i1038.photobucket.com/albums/a467/kanye_brown/analysis_1.jpg?t=1306280360

a) prove the set U(d1,...,dp) is an open subset of X.

b) Prove that U is a basis of open sets for (X, d).

c) Say whether the statement is true or false.

Consider the following statement: “For every p 2 N and every d1, . . . , dp ϵ {0, 1},

the set U(d1,...,dp) is a closed subset of X.”

Is the statement true? Justify your answer (with a proof or counterexample).

Any ideas?

2. Relevant equations

3. The attempt at a solution

I'm not sure where to start. I know (X,d) is a metric space but that's about it so far.

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# Hamming metric

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