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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

( 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

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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exercise 1 part 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
Transcribed Image Text:( 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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