Let X = {a, b, c}, T1 = {X, p, {a}, {b}, {a,b}} and T2 = {X, p, {a}, {c}, {a,c}}. Then one of the following is true: * the smallest topology on X containing both T1 and T2 is the discrete topology. O T1UT2 is a topology on X but T1NT2 is not T1NT2 and T1UT2 are both topologies on T1NT2 and T1UT2 both cannot be topologies on X

Let X = {a, b, c}, T1 = {X, p, {a}, {b}, {a,b}} and T2 = {X, p, {a}, {c}, {a,c}}. Then one of the following is true: * the smallest topology on X containing both T1 and T2 is the discrete topology. O T1UT2 is a topology on X but T1NT2 is not T1NT2 and T1UT2 are both topologies on T1NT2 and T1UT2 both cannot be topologies on X

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Let X = {a, b, c}, T1 = {X, þ, {a}, {b}, {a,b}} and
T2 = {X, ô, {a}, {c}, {a,c}}. Then one of the
following is true: *
the smallest topology on X containing both
T1 and T2 is the discrete topology.
O T1UT2 is a topology on X but T1NT2 is not
T1NT2 and T1UT2 are both topologies on
T1NT2 and T1UT2 both cannot be
topologies on X

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