alfa O & 0a E 3:00 PM 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...


alfa O &<br>0a E 3:00 PM<br>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>[0,1] is not homeomorphic to ]0,1[<br>Ris homeomorphic to ]0, +o[<br>Ris homeomorphic to ]0,1[<br>O 1-0,0] is homeomorphic to [0,+ oo[<br>< O O<br>

Extracted text: alfa O & 0a E 3:00 PM 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 [0,1] is not homeomorphic to ]0,1[ Ris homeomorphic to ]0, +o[ Ris homeomorphic to ]0,1[ O 1-0,0] is homeomorphic to [0,+ oo[ < o="">

Jun 05, 2022
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