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Separation properties inX and 2X. Upper semicontinuous and measurable multifunctions

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Abstract

This paper investigates relations among some separation (countable separation) properties of a topological space (X, τ X ), corresponding properties of the hyperspace 2X, endowed with the finite topology (the σ-algebra σ(ν +)), and closedness (measurability) of graphs of semicontinuous (measurable) multifunctions.

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References

  1. Davis A.S.,Indexed systems of neighborhoods for general topological spaces, Amer. Math. Monthly,68 (1961), 886–893.

    Article  MATH  MathSciNet  Google Scholar 

  2. Franklin S.P., Sorgenfrey R.H.,Closed and image-closed relations, Pac. J. Math.,19 n. 3 (1966), 433–439.

    MATH  MathSciNet  Google Scholar 

  3. Halmos P.R.,Measure theory, Van Nostrand, N.Y., 1950.

    MATH  Google Scholar 

  4. Hou S.H.,Implicit function theorem in topological spaces, Appl. Analysis,13 (1982), 209–217.

    Article  MATH  Google Scholar 

  5. Joseph J.E.,Regularity, normality and weak continuity for multifunctions, Math. Japonica26 n. 6 (1981), 647–651.

    MATH  Google Scholar 

  6. Kuratowski K.,Topology, vol. 1, Academic Press, New York and London, 1966.

    Google Scholar 

  7. Michael E.,Topologies on spaces of subsets, Trans. Amer. Math. Soc.,71 (1951), 152–182.

    Article  MATH  MathSciNet  Google Scholar 

  8. Wagner D.H.,Survey of measurable selection theorems, SIAM J. Control and Optimization,15 n. 5 (1977), 859–903.

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Dipartimento di Matematica ed Applicazioni, Via Archirafi, 34, 90123, Palermo

    Diego Averna

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  1. Diego Averna
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Averna, D. Separation properties inX and 2X. Upper semicontinuous and measurable multifunctions. Rend. Circ. Mat. Palermo 38, 140–151 (1989). https://doi.org/10.1007/BF02844856

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  • DOI: https://doi.org/10.1007/BF02844856

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