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A topological space X is zero ? dimensional if it has a basis B consisting of...

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Advance Math

A topological space X is zero ? dimensional if it has a basis Bconsisting of open sets which are simultaneously closed. (a) Provethat the set C = {0, 1}N with the product topology iszero-dimensional. (b) Prove that if (X, d) is a metric space forwhich |X| < |R|, that is the cardinality of X is less than thatof R, then X is zero-dimensional.

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