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(2.1) Consider the following topologies on X = {a, b, c, d} and Y = {r, y, z, w} TX = {X,0, {a} , {a,b}, {a, b, c}} and ty = {Y, 0, {x}, {y},{r, y}, {y, z, w}}. Also consider the functions f: X Y and g:X Y defined by the diagrams below: d. (a) Show thatf is continuous, (b) Is g continuous? Motivate your answer.

(2.1) Consider the following topologies on X = {a, b, c, d} and Y = {r, y, z, w} TX = {X,0, {a} , {a,b}, {a, b, c}} and ty = {Y, 0, {x}, {y},{r, y}, {y, z, w}}. Also consider the functions f: X Y and g:X Y defined by the diagrams below: d. (a) Show thatf is continuous, (b) Is g continuous? Motivate your answer.

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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(2.1) Consider the following topologies on X = {a, b, c, d} and Y = {r, y, z, w} TX = {X,0, {a} , {a,b}, {a, b, c}} and ty = {Y,0, {r} , {y},{r, y}, {y, z, w}}. Also consider the functions f :X Y and g:X Y defined by the diagrams below : %3D d. (a) Show thatf is continuous, (b) Is g continuous? Motivate your answer.
Transcribed Image Text:(2.1) Consider the following topologies on X = {a, b, c, d} and Y = {r, y, z, w} TX = {X,0, {a} , {a,b}, {a, b, c}} and ty = {Y,0, {r} , {y},{r, y}, {y, z, w}}. Also consider the functions f :X Y and g:X Y defined by the diagrams below : %3D d. (a) Show thatf is continuous, (b) Is g continuous? Motivate your answer.
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