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5) We have seen that the collection of subsets of Z given by = {B(n) | B(n) = {n} when n is odd and B(n) = {n – 1, n, n + 1} when n is even} forms a basis for a topology on Z, the digital line topology. Can a set of precisely four consecutive integers ever be open in this topology? Explain your answer.

5) We have seen that the collection of subsets of Z given by = {B(n) | B(n) = {n} when n is odd and B(n) = {n – 1, n, n + 1} when n is even} forms a basis for a topology on Z, the digital line topology. Can a set of precisely four consecutive integers ever be open in this topology? Explain your answer.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 11E: Let be a relation defined on the set of all integers by if and only if sum of and is odd. Decide...
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we have seen that

(a, b) = {x E R|a < x < b}; [a, b) = {x E R|a <x <b}; (a, b] = {x ER la < x < b} and [a, b] = {x € R[a <x< b}
Transcribed Image Text:(a, b) = {x E R|a < x < b}; [a, b) = {x E R|a <x <b}; (a, b] = {x ER la < x < b} and [a, b] = {x € R[a <x< b}
5) We have seen that the collection of subsets of Z given by B= {B(n)|B(n) = {n} when n is odd and B(n) = {n – 1, n, n + 1} when n is even} forms a basis for a topology on Z, the digital line topology. Can a set of precisely four consecutive integers ever be open in this topology? Explain your answer.
Transcribed Image Text:5) We have seen that the collection of subsets of Z given by B= {B(n)|B(n) = {n} when n is odd and B(n) = {n – 1, n, n + 1} when n is even} forms a basis for a topology on Z, the digital line topology. Can a set of precisely four consecutive integers ever be open in this topology? Explain your answer.
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