Let X = {1, 2, 3, 4, 5, 6} and let T1 = {X, %3D 4, {2}, {1,2}, {2,3,4}, {1, 2,3,4}} and T2 = {X, þ, {2}, {1,2,3}, {4,5,6}, {2,4,5,6}} * T1 and T2 are both not topologies on X T1 is a topology on X and T2 is not a topology on X O 11 and T2 are both topologies on X T1 is not a topology and T2 is a topology on X o O

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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Let X = {1, 2, 3, 4, 5, 6} and let T1 = {X,
þ, {2}, {1,2}, {2,3,4}, {1, 2,3,4}} and T2 :
{X, þ, {2}, {1,2,3}, {4,5,6}, {2,4,5,6}}
T1 and T2 are both not topologies
on X
T1 is a topology on X and T2 is not a
topology on X
T1 and T2 are both topologies on X
T1 is not a topology and T2 is a
topology on X
Transcribed Image Text:Let X = {1, 2, 3, 4, 5, 6} and let T1 = {X, þ, {2}, {1,2}, {2,3,4}, {1, 2,3,4}} and T2 : {X, þ, {2}, {1,2,3}, {4,5,6}, {2,4,5,6}} T1 and T2 are both not topologies on X T1 is a topology on X and T2 is not a topology on X T1 and T2 are both topologies on X T1 is not a topology and T2 is a topology on X
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