Calculate the relative (sub-space) topology with respect to the usual (metric) topology in R (the set...

Calculate the relative (sub-space) topology with respect to the usual (metric) topology in R (the set of real numbers), for the following sub-sets of R:

X = Z, where Z represents the set of integers

Y = {0} U {1 / n | n is an integer such that n> 0}

Calculate (establish who are) the closed (relative) sets for the X and Y sub-spaces defined above.

Is {0} open relative to X?

Is {0} open relative to Y?

Expert Solution

Colby Messinger answered 9 months ago

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