10. Let (X, Tx) and (Y, Ty) be two topological spaces, such that X = (a, b,c, d}, Tx = (o, X, (a}, {a, b}, (a,b,c}} Y = {1,2,3, 4}, Ty {6.Y, (2). (2,3, 4}} %3D Consider the functions f: XY and g: XY defined by f(a) = f(b) = 2, f(e) = 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
10. Let (X, Tx) and (Y, Ty) be two topological spaces, such that X = (a, b,c, d}, Tx = (o, X, (a}, {a, b}, (a,b,c}} Y = {1,2,3, 4}, Ty {6.Y, (2). (2,3, 4}} %3D Consider the functions f: XY and g: XY defined by f(a) = f(b) = 2, f(e) = 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
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
![10. Let (X, Tx) and (Y, Ty) be two topological spaces, such that
X = {a, b,c, d}, Tx = {ó, 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: XY defined by
f(a) = f(b) = 2, f (c) = 4, ƒ(d) = 3
g(a) = g(b) = g(d) = 2, g(c) = 3
Then
(a) ƒ and g are both continuous
(b) f and g are both discontinuous
(c) f is discontinuous and g is continuous
(d) f is contimuous and g is discontinuous](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdb1d8b9c-ad9e-4ade-aace-5ac43ba5e166%2F62403b73-7094-42ac-ad75-83a6308ba0ac%2F9ls47ya_processed.jpeg&w=3840&q=75)
Transcribed Image Text:10. Let (X, Tx) and (Y, Ty) be two topological spaces, such that
X = {a, b,c, d}, Tx = {ó, 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: XY defined by
f(a) = f(b) = 2, f (c) = 4, ƒ(d) = 3
g(a) = g(b) = g(d) = 2, g(c) = 3
Then
(a) ƒ and g are both continuous
(b) f and g are both discontinuous
(c) f is discontinuous and g is continuous
(d) f is contimuous and g is discontinuous
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