Let X = {a, b, c, d} and T = { X, p, {a,b},%3D{c,d}}, thenAn open proper subset of X may beclopen and may be not.Every open subset of X is clopenAn open proper subset of X cannot beclopenO None of the choicesO O Let X = {1, 2, 3, 4, 5, 6} and let T1 = {X, p,{3}, {1,2,3}, {2,3,4}, {2}} and T2 = {X, ¢, {2},%3D{1,2,3}, {4,5,6}, {2,4,5,6}} *T1 is a topology on X and T2 is not atopology on XT1 and T2 are both not topologies onXO T1 and T2 are both topologies on XT1 is not a topology and T2 is atopology on X

To find the true options for the given questions. Definitions: 1. Open sets can be defined as the…

Let X = {a, b, c, d} and T = { X, p, {a,b}, {c,d}}, then * An open proper subset of X may be clopen and may be not. Every open subset of X is clopen An open proper subset of X cannot be clopen O None of the choices O O O

Let X = {a, b, c, d} and T = { X, p, {a,b}, {c,d}}, then * An open proper subset of X may be clopen and may be not. Every open subset of X is clopen An open proper subset of X cannot be clopen O None of the choices O O O

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, d} and T = { X, p, {a,b},
%3D
{c,d}}, then
An open proper subset of X may be
clopen and may be not.
Every open subset of X is clopen
An open proper subset of X cannot be
clopen
O None of the choices
O O

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

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