A property is said to be a topological property if it is preserved by homeomorphism. Suppose that R is equipped with the usual topology, then the boundedness and the closedness are not topological properties because * Ris homeomorphic to ]-co, O[ Ris homeomorphic to Ja,b[ O [a,b] is not homeomorphic to Ja,b[ Ris homeomorphic to ]-o, 0]

A property is said to be a topological property if it is preserved by homeomorphism. Suppose that R is equipped with the usual topology, then the boundedness and the closedness are not topological properties because * Ris homeomorphic to ]-co, O[ Ris homeomorphic to Ja,b[ O [a,b] is not homeomorphic to Ja,b[ Ris homeomorphic to ]-o, 0]

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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A property is said to be a topological property if it is preserved by homeomorphism. Suppose that R is equipped with the usual topology, then the boundedness and the closedness are not topological properties because O 1-00,0] is homeomorphic to [0,+[ O Ris homeomorphic to ]0, +[ R is homeomorphic to ]0,1[ [0,1] is not homeomorphic to ]0,1[
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