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 1-00,0] is homeomorphic to [0,+[<br>O Ris homeomorphic to ]0, +[<br>R is homeomorphic to ]0,1[<br>[0,1] is not homeomorphic to ]0,1[<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 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[

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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