- #1
Metric_Space
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Homework Statement
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?
Homework Equations
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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