0. Let (X, Tx) and (Y, Ty) be two topological spaces, such thatX = {a, b, c, d}, Tx = {ø, X, {a}, {a, b}, {a, b, c}}Y = {1,2,3, 4}, Ty%3D%3D= {6,Y, {2}, {2,3, 4}}%3D%3DConsider the functions f: X →Y and g: X →Y defined byf(a) = f(b) = 2, f(c) = 4, f(d) = 3%3D%3D%3Dg(a) = g(b) = g(d) = 2, g(c) = 3%3D%3D%3DThen(a) f and g are both continuous(b) f and g are both discontinuous(c) f is discontinuous and g is continuous(d) f is continuous and g is discontinuous

We need to check the necessary and sufficient conditions for continuity

Let (X, Tx) and (Y, Ty) be two topological spaces, such that X = {a, b, c, d}, Tx = {ø, X, {a}, {a, b}, {a, b, c} Y = {1,2, 3, 4}, Ty = {ó,Y, {2}, {2, 3, 4}} %3D %3D Consider the functions f: XY and g: X Y defined by f(a) = f(b) = 2, f(c) = 4, f(d) = 3 %3D %3D %3D g(a) = g(b) = 9(d) = 2, g(c) = 3 %3D %3D %3D Then (a) f and g are both continuous (b) f and g are both discontinuous (c) f is discontinuous and g is continuous (d) f is continuous and g is discontinuous

Let (X, Tx) and (Y, Ty) be two topological spaces, such that X = {a, b, c, d}, Tx = {ø, X, {a}, {a, b}, {a, b, c} Y = {1,2, 3, 4}, Ty = {ó,Y, {2}, {2, 3, 4}} %3D %3D Consider the functions f: XY and g: X Y defined by f(a) = f(b) = 2, f(c) = 4, f(d) = 3 %3D %3D %3D g(a) = g(b) = 9(d) = 2, g(c) = 3 %3D %3D %3D Then (a) f and g are both continuous (b) f and g are both discontinuous (c) f is discontinuous and g is continuous (d) f is continuous and g is discontinuous

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

0. Let (X, Tx) and (Y, Ty) be two topological spaces, such that
X = {a, b, c, d}, Tx = {ø, X, {a}, {a, b}, {a, b, c}}
Y = {1,2,3, 4}, Ty
%3D
%3D
= {6,Y, {2}, {2,3, 4}}
%3D
%3D
Consider the functions f: X →Y and g: X →Y defined by
f(a) = f(b) = 2, f(c) = 4, f(d) = 3
%3D
%3D
%3D
g(a) = g(b) = g(d) = 2, g(c) = 3
%3D
%3D
%3D
Then
(a) f and g are both continuous
(b) f and g are both discontinuous
(c) f is discontinuous and g is continuous
(d) f is continuous and g is discontinuous

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