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...

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

Extracted text: 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 [a,b] is not homeomorphic to ]a,b[ Ris homeomorphic to la,b[ Ris homeomorphic to ]-o, 0[ Ris homeomorphic to ]-0, 0]

Jun 05, 2022

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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...

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