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Let (X, Tx) and (Y, Ty) be two topological spaces, such that X = {a, b,c, d}, Tx = {6, X, {a}, {a, b}, {a, b, c}} Y = {1,2, 3, 4}, Ty = {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 g(a) = g(b) = g(d) = 2, g(c) = 3 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 = {6, X, {a}, {a, b}, {a, b, c}} Y = {1,2, 3, 4}, Ty = {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 g(a) = g(b) = g(d) = 2, g(c) = 3 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
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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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 = {0,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 g(a) = g(b) = g(d) 2, g(c) = 3 %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
Transcribed Image Text: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 = {0,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 g(a) = g(b) = g(d) 2, g(c) = 3 %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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