Let X = (a, b, c, d) and TX = (Ø, X, (b), {b.c), {a,b,d}) be a topology 3, 4) and TY = (0, Y, (3), {1,2,3} } be a topology on Y. Let f be a mapping from X into Y defined by f(a)=f(b) 3 3, f(c) = 2 and f(d) = 1. Letg be mapping from X into Y defined by g(a) = 1. g(b)=g(c)=3 and g(d) = 2. Then O fis not continuous andg is continuous O fand g are not continuotis O fand g are both continuous O fis continuous and g is not continuous
Let X = (a, b, c, d) and TX = (Ø, X, (b), {b.c), {a,b,d}) be a topology 3, 4) and TY = (0, Y, (3), {1,2,3} } be a topology on Y. Let f be a mapping from X into Y defined by f(a)=f(b) 3 3, f(c) = 2 and f(d) = 1. Letg be mapping from X into Y defined by g(a) = 1. g(b)=g(c)=3 and g(d) = 2. Then O fis not continuous andg is continuous O fand g are not continuotis O fand g are both continuous O fis continuous and g is not continuous
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 = (a, b, c, d) and TX = (0, X, (b), (b.c), {a,b,d)}) be a topology on X. Let Y = {1, 2,
3, 4) and TY = (Ø, Y, (3), (1,2,3}} be a topology on Y. Let f be a mapping from X into
Y defined by f(a)-f(b) = 3, f(c) = 2 and f(d) = 1. Let g be mapping from X intoY
defined by g(a)-1.g(b)-g(c)=3 and g(d) = 2. Then
fis not .continuous and g is contimuous
fand g are not continuous
fand g are both continuous
O fis continuous and g is not continuous](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb1d396a1-c213-484c-9c1f-84f8f76faad3%2F038c9c0a-7fb2-4be9-8fe8-e9eb018f95ae%2Fzaby65m_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let X = (a, b, c, d) and TX = (0, X, (b), (b.c), {a,b,d)}) be a topology on X. Let Y = {1, 2,
3, 4) and TY = (Ø, Y, (3), (1,2,3}} be a topology on Y. Let f be a mapping from X into
Y defined by f(a)-f(b) = 3, f(c) = 2 and f(d) = 1. Let g be mapping from X intoY
defined by g(a)-1.g(b)-g(c)=3 and g(d) = 2. Then
fis not .continuous and g is contimuous
fand g are not continuous
fand g are both continuous
O fis continuous and g is not continuous
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