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On the Normed Linear Space of Hausdorff Continuous Functions

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Large-Scale Scientific Computing (LSSC 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3743))

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Abstract

In the present work we show that the linear operations in the space of Hausdorff continuous functions are generated by an extension property of these functions. We show that the supremum norm can be defined for Hausdorff continuous functions in a similar manner as for real functions, and that the space of all bounded Hausdorff continuous functions on an open set is a normed linear space. Some issues related to approximations in the space of Hausdorff continuous functions by subspaces are also discussed.

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Author information

Authors and Affiliations

  1. University of Pretoria, Pretoria, 0002, South Africa

    Roumen Anguelov

  2. Institute of Mathematics and Informatics, BAS, Acad. G. Bonchev, block 8, 1113, Sofia, Bulgaria

    Svetoslav Markov

  3. Bulgarian Embassy, 36-3, Yoyogi 5-chome, Shibuia-ku, Tokyo, 151-0053, Japan

    Blagovest Sendov

Authors
  1. Roumen Anguelov
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  2. Svetoslav Markov
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  3. Blagovest Sendov
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Editor information

Editors and Affiliations

  1. Institute for Parallel Processing, Bulgarian Academy of Sciences, Acad. G. Bonchev, Bl. 25A, 1113, Sofia, Bulgaria

    Ivan Lirkov

  2. Institute for Parallel Processing, Bulgarian Academy of Sciences, Acad. G. Bonchev Str. Bl. 25-A, 1113, Sofia, Bulgaria

    Svetozar Margenov

  3. Informatics & Mathematical Modeling, Technical University of Denmark, DK-2800, Lyngby, Denmark

    Jerzy Waśniewski

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© 2006 Springer-Verlag Berlin Heidelberg

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Anguelov, R., Markov, S., Sendov, B. (2006). On the Normed Linear Space of Hausdorff Continuous Functions. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds) Large-Scale Scientific Computing. LSSC 2005. Lecture Notes in Computer Science, vol 3743. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11666806_31

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  • DOI: https://doi.org/10.1007/11666806_31

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-31994-8

  • Online ISBN: 978-3-540-31995-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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