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...

Topology
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,<br>then the boundedness and the<br>closedness are not topological<br>properties because<br>O [a,b] is not homeomorphic to ]a,b[<br>Ris homeomorphic to ]-o, 0[<br>Ris homeomorphic to ]-0o, 0]<br>Ris homeomorphic to ]a,b[<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 ]-o, 0[ Ris homeomorphic to ]-0o, 0] Ris homeomorphic to ]a,b[

Jun 05, 2022
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