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Ideal Banach category theorems and functions

Zbigniew Piotrowski (1997)

Mathematica Bohemica

Based on some earlier findings on Banach Category Theorem for some “nice” σ -ideals by J. Kaniewski, D. Rose and myself I introduce the h operator ( h stands for “heavy points”) to refine and generalize kernel constructions of A. H. Stone. Having obtained in this way a generalized Kuratowski’s decomposition theorem I prove some characterizations of the domains of functions having “many” points of h -continuity. Results of this type lead, in the case of the σ -ideal of meager sets, to important statements...

Induced mappings on hyperspaces F n K ( X )

Enrique Castañeda-Alvarado, Roberto C. Mondragón-Alvarez, Norberto Ordoñez (2024)

Commentationes Mathematicae Universitatis Carolinae

Given a metric continuum X and a positive integer n , F n ( X ) denotes the hyperspace of all nonempty subsets of X with at most n points endowed with the Hausdorff metric. For K F n ( X ) , F n ( K , X ) denotes the set of elements of F n ( X ) containing K and F n K ( X ) denotes the quotient space obtained from F n ( X ) by shrinking F n ( K , X ) to one point set. Given a map f : X Y between continua, f n : F n ( X ) F n ( Y ) denotes the induced map defined by f n ( A ) = f ( A ) . Let K F n ( X ) , we shall consider the induced map in the natural way f n , K : F n K ( X ) F n f ( K ) ( Y ) . In this paper we consider the maps f , f n , f n , K for some K F n ( X ) and f n , K for...

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