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Q2) True or false (1) B = {(a), (b), {c}} is a base of the discrete topology on X = (a, b, c). (X,p.(x,y), (x, z). (y, z)} is not a topology on X (x, y,z). (3) For X = (a, b, c), the excluding point topology is E, {x,q.(a), (c), (a,c), (a, b}}. %3! %3D (2) T= %3D (4) For a discrete topology on X and o AC X. the closure of A is 4.

Q2) True or false (1) B = {(a), (b), {c}} is a base of the discrete topology on X = (a, b, c). (X,p.(x,y), (x, z). (y, z)} is not a topology on X (x, y,z). (3) For X = (a, b, c), the excluding point topology is E, {x,q.(a), (c), (a,c), (a, b}}. %3! %3D (2) T= %3D (4) For a discrete topology on X and o AC X. the closure of A is 4.

Advanced Engineering Mathematics
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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Q2) True or false (1) B = {(a), (b}, {c}} is a base of the discrete topology on X = (a, b. c). (2) T (X,q.(x,y}). (x, z). (y. z)} is not a topology on X = (x, y, z). (3) For X = (a, b,c), the excluding point topology is E, = {X, p. (a), (c), (a, c), (a, b}}. (4) For a discrete topology on X and p AcX, the closure of A is A. (5) For an indiscrete topology on X (a, b,c) and A {a, b), the limit points of A is (a, b). (6) For the usual topology on R and A (2,5), the interior points of A is (2, 5). (7) For a cofinite topology on X and a finite subset A of X, the exterior points of A is A°. (8) B = {{a, b), (a, c}} is a base for a topology t on X = {a, b, c, d). (9) Every subspace of a discrete space is discrete. %3! !! %3D (10) b(A) = An (A°)
Transcribed Image Text:Q2) True or false (1) B = {(a), (b}, {c}} is a base of the discrete topology on X = (a, b. c). (2) T (X,q.(x,y}). (x, z). (y. z)} is not a topology on X = (x, y, z). (3) For X = (a, b,c), the excluding point topology is E, = {X, p. (a), (c), (a, c), (a, b}}. (4) For a discrete topology on X and p AcX, the closure of A is A. (5) For an indiscrete topology on X (a, b,c) and A {a, b), the limit points of A is (a, b). (6) For the usual topology on R and A (2,5), the interior points of A is (2, 5). (7) For a cofinite topology on X and a finite subset A of X, the exterior points of A is A°. (8) B = {{a, b), (a, c}} is a base for a topology t on X = {a, b, c, d). (9) Every subspace of a discrete space is discrete. %3! !! %3D (10) b(A) = An (A°)
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