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Characterization of quasi-continuity of multifunctions of two variables

  • Olena Fotiy EMAIL logo , Oleksandr Maslyuchenko and Vasyľ Nesterenko
Published/Copyright: April 30, 2016
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 66 Issue 1

Abstract

We prove that a compact-valued multifunction F: X × Y → Z, where X is a Baire space and Y, Z are separable metrizable spaces, is quasi-continuous if and only if F is horizontally quasi-continuous and there exists an residual subset M of X such that for any x ∈ M the multifunction Fx = F(x, ·) is quasi-continuous on Y.

Keywords: multifunction; upper quasi-continuity; lower quasi-continuity; symmetrically upper quasi-continuity; symmetrically lower quasi-continuity; upper horizontally quasi-continuity; lower horizontally quasi-continuity
MSC: Primary 54C08; 54C60

  1. This paper has been communicated by L'ubica Holá

References

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Received: 2013-2-18
Accepted: 2013-6-10
Published Online: 2016-4-30
Published in Print: 2016-2-1

© 2016 Mathematical Institute Slovak Academy of Sciences

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https://doi.org/10.1515/ms-2015-0135
Keywords for this article
multifunction; upper quasi-continuity; lower quasi-continuity; symmetrically upper quasi-continuity; symmetrically lower quasi-continuity; upper horizontally quasi-continuity; lower horizontally quasi-continuity

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  3. Research Article
  4. On the number of slim, semimodular lattices
  5. Research Article
  6. Quantum computational algebra with a non-commutative generalization
  7. Research Article
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  9. Research Article
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  11. Research Article
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  13. Research Article
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