Observe that if (X, T) is a discrete space or an indiscrete space, then every open = set is a clopen set. Find a topology T on the set X : {a, b, c, d} which is not discrete and is not indiscrete but has the property that every open set is clopen.
Observe that if (X, T) is a discrete space or an indiscrete space, then every open = set is a clopen set. Find a topology T on the set X : {a, b, c, d} which is not discrete and is not indiscrete but has the property that every open set is clopen.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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![Observe that if (X, T) is a discrete space or an indiscrete space, then every open
set is a clopen set. Find a topology T on the set X = {a, b, c, d} which is not
discrete and is not indiscrete but has the property that every open set is clopen.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5bb1c67f-de63-4ad1-ada9-056d2565b4d2%2Fd382147c-f6d3-438a-98b8-74f5bef5c89a%2Fkr2aya7_processed.png&w=3840&q=75)
Transcribed Image Text:Observe that if (X, T) is a discrete space or an indiscrete space, then every open
set is a clopen set. Find a topology T on the set X = {a, b, c, d} which is not
discrete and is not indiscrete but has the property that every open set is clopen.
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