2. Let X = {a, b, c, d, e, f}. Which of the following collections of subsets of X is a topology on X? (Justify your answers.) (a) T1 = {X, Ø, {c}, {b, d, e}, {b,c, d, e}, {b}}; (b) T2 = {X, Ø, {a}, {b, d, e}, {a, b, d}, {a,b, d, e}}; (c) T3 = {X, Ø, {b}, {a, b, c}, {d,e, f}, {b, d, e, f}}.

2. Let X = {a, b, c, d, e, f}. Which of the following collections of subsets of X is a topology on X? (Justify your answers.) (a) T1 = {X, Ø, {c}, {b, d, e}, {b,c, d, e}, {b}}; (b) T2 = {X, Ø, {a}, {b, d, e}, {a, b, d}, {a,b, d, e}}; (c) T3 = {X, Ø, {b}, {a, b, c}, {d,e, f}, {b, d, e, f}}.

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

topologie

2. Let X = {a, b, c, d, e, ƒ}. Which of the following collections of subsets of X is a
topology on X? (Justify your answers.)
(a) T1 = {X, Ø, {c}, {b, d, e}, {b,c, d, e }, {b}}:
(b) T2 = {X, Ø, {a}, {b, d, e}, {a, b, d}, {a,b, d, e}};
(c) T3 = {X, Ø, {b}, {a, b, c}, {d,e, ƒ}, {b, d, e, f}}.

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