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[ O Ris homeomorphic to 1-, O[ R is homeomorphic to ]-0, 0] R is homeomorphic to Ja,b[

Advanced Engineering Mathematics
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ISBN:9780470458365
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Chapter2: Second-order Linear Odes
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f is not continuous and g is continuous
O fandg are both continuous
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 *
[a,b] is not homeomorphic to Ja,b[
R is homeomorphic to ]-, O[
R is homeomorphic to ]-0, 0]
R is homeomorphic to Ja,b[
Which one of the following statements is true? *
R with the Euclidean topology and R with the discrete topology are not homeomorphic
None of the choices
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Transcribed Image Text:f is not continuous and g is continuous O fandg are both continuous 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 * [a,b] is not homeomorphic to Ja,b[ R is homeomorphic to ]-, O[ R is homeomorphic to ]-0, 0] R is homeomorphic to Ja,b[ Which one of the following statements is true? * R with the Euclidean topology and R with the discrete topology are not homeomorphic None of the choices search
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