exercise 1part 4 only (1) Give an example of a compact space which is not Hausdorff.2) Give an example of a locally compact space which is not compact.3) Give an example of a connected space which is not path-connected.4) Give an example of a topological space which is not a Baire space.TAUT

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Answered: ( 1) Give an example of a compact 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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( 1) Give an example of a compact space which is not Hausdorff. 2) Give an example of a locally compact space which is not compact. 3) Give an example of a connected space which is not path-connected. 4) Give an example of a topological space which is not a Baire space. TAUT