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Uniform Continuity of Multifunctions

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Abstract

The main objective of this article is to introduce a global version of continuity of multifunctions. Such a family of multifunctions is called uniformly continuous. Equivalent characterizations and various interesting properties of uniformly continuous multifunctions are studied in detail.

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References

  1. Atsuji, M.: Uniform continuity of continuous functions of metric spaces. Pac. J. Math. 8, 11–16 (1958)

    Article  MathSciNet  Google Scholar 

  2. Beer, G.: Topologies on Closed and Closed Convex Sets. Mathematics and Its Applications, vol. 268. Kluwer Academic, Dordrecht (1993)

    Book  Google Scholar 

  3. Fedorchuk, V.V., Künzi, H.-P.A.: Uniformly open mappings and uniform embeddings of function spaces. Topol. Appl. 61(1), 61–84 (1995)

    Article  MathSciNet  Google Scholar 

  4. Hejcman, J.: Boundedness in uniform spaces and topological groups. Czechoslov. Math. J. 9(84), 544–563 (1959)

    Article  MathSciNet  Google Scholar 

  5. Holý, D.: Uniform convergence on spaces of multifunctions. Math. Slovaca 57(6), 561–570 (2007)

    Article  MathSciNet  Google Scholar 

  6. Klein, E., Thompson, A.: Theory of Correspondences. Wiley, New York (1984)

    Google Scholar 

  7. Kundu, S., Jain, T.: Atsuji spaces: equivalent conditions. Topol. Proc. 30(1), 301–325 (2006)

    MathSciNet  Google Scholar 

  8. Lechicki, A.: On bounded and subcontinuous multifunctions. Pac. J. Math. 75(1), 191–197 (1978)

    Article  MathSciNet  Google Scholar 

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Acknowledgements

The author would like to thank the referee for various valuable suggestions, especially for suggesting Corollary 5 and Proposition 7.

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No funding was received for conducting this study.

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Authors and Affiliations

  1. Department of Mathematics, St. Stephen’s College, 110007, Delhi, India

    Manisha Aggarwal

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  1. Manisha Aggarwal
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Correspondence to Manisha Aggarwal.

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Aggarwal, M. Uniform Continuity of Multifunctions. Set-Valued Var. Anal 32, 11 (2024). https://doi.org/10.1007/s11228-024-00714-6

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  • DOI: https://doi.org/10.1007/s11228-024-00714-6

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