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.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
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}](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4035242d-f18b-4709-bb6e-951753bf8b42%2F714ce770-ec10-453a-9e12-cb4e46fd2405%2Fu7ueb52_processed.jpeg&w=3840&q=75)
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}
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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