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A Continuous Bijection from ℓ2 onto a Subset of ℓ2 Whose Inverse Is Everywhere Discontinuous

Sam H. Creswell
The American Mathematical Monthly
Vol. 117, No. 9 (November 2010), pp. 823-828
DOI: 10.4169/000298910x521698
Stable URL: http://www.jstor.org/stable/10.4169/000298910x521698
Page Count: 6
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A Continuous Bijection from ℓ2 onto a Subset of ℓ2 Whose Inverse Is Everywhere Discontinuous
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Abstract

Abstract We show that the series equivalent of a Lebesgue integral used by Mazur to develop a homeomorphism gives a continuous bijection whose inverse is everywhere discontinuous.

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