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Representation of Continuous Functions and Its Applications

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Abstract

In this work, we introduce a Representation of continuous real-valued functions defined over a real Hilbert space. As a consequence, we can introduce a Sandwich Theorem for semi-continuous functions, a Separation Theorem for closed sets and a representation Theorem of lower semi-continuous functions.

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Acknowledgements

The author is thankful to CNPq for the grant “Productividade em pesquisa—PQ—2012”, to IMPA, where this work started in January of 2012, and to UCB, where the development took place. The author is also thankful to Fernanda Raupp from PUC-Rio and an anonymous referee for their suggestions, which improved this manuscript.

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  1. Graduate School in Economics, Catholic University of Brasilia, SGAN 916, Modulo B, 70790-000, Brasilia, DF, Brazil

    Wilfredo Sosa

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  1. Wilfredo Sosa
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Correspondence to Wilfredo Sosa.

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Sosa, W. Representation of Continuous Functions and Its Applications. J Optim Theory Appl 159, 795–804 (2013). https://doi.org/10.1007/s10957-013-0375-8

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  • DOI: https://doi.org/10.1007/s10957-013-0375-8

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