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- W4387364117 abstract "We present new properties of the set functions K and T, some of them using the property of Kelley. In particular, we show that the continuity of T on continua implies the continuity of K on continua, for continua with the property of Kelley. We also give a sufficient condition for the idempotency of K on closed sets and present an example showing the condition is not necessary. In particular, we have that for continua with the property of Kelley, K is idempotent on closed sets. We prove that for the case of metric continua, the family of K-closed sets is a Gδ subset of the hyperspace of nonempty closed sets of the continuum, in particular, it is completely metrizable. We also show that the image of the hyperspaces of nonempty closed subsets under K is an analytic set. We prove a characterization of the continuity of T on continua for the class of continua with the property of Kelley." @default.
- W4387364117 created "2023-10-06" @default.
- W4387364117 creator A5028444212 @default.
- W4387364117 date "2024-01-01" @default.
- W4387364117 modified "2023-10-18" @default.
- W4387364117 title "The Set Functions <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML altimg=si1.svg><mml:mi mathvariant=script>K</mml:mi></mml:math> and <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML altimg=si2.svg><mml:mi mathvariant=script>T</mml:mi></mml:math> and the Property of Kelley" @default.
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- W4387364117 doi "https://doi.org/10.1016/j.topol.2023.108747" @default.
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