Define a collection T of subsets of Z+ as follows: W ∈ T if and only if n ∈ W implies that all positive divisors of n are also elements of W. Verify that T is a topology on Z+. In this topology find Cl({1}) and Cl({2}).

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Define a collection T of subsets of Z+ as follows:
W ∈ T if and only if n ∈ W implies that all positive divisors of n are also elements of W.

Verify that T is a topology on Z+. In this topology find Cl({1}) and Cl({2}).

Expert Solution
Step 1

Given Z+the set of positive integers.

T is the collections of subsets W of Z+ such that

W={mZ+: m/n; when nW}, Where m/n implies m divides n and m>0

 

 

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