Exercise 3Part 4 4) If X is a non-empty Baire space, which is Hausdorff and without isolated points. If (Y, d) is ametric space and f: X→ Y is a map, show thatCont (f) = {x X| f is continuous at X},the set of points in X at whichis continuous, cannot be dense and countable.

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Answered: 4) If X is a non-empty Baire space,…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.2: Vector Spaces

Problem 38E: Determine whether the set R2 with the operations (x1,y1)+(x2,y2)=(x1x2,y1y2) and c(x1,y1)=(cx1,cy1)...

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4) If X is a non-empty Baire space, which is Hausdorff and without isolated points. If (Y, d) is a metric space and f: X→Y is a map, show that Cont (f) = {x X| f is continuous at X}, the set of points in X at which is continuous, cannot be dense and countable.