Corpus ID: 237490316

Games characterizing certain families of functions

  title={Games characterizing certain families of functions},
  author={Marek Balcerzak and Tomasz Natkaniec and Piotr Szuca},
We obtain several game characterizations of Baire 1 functions between Polish spaces X, Y which extends the recent result of V. Kiss. Then we propose similar characterizations for equi-Bare 1 families of functions. Also, using related ideas, we give game characterizations of Baire measurable and Lebesgue measurable functions. 


Playing in the first Baire class
A self-contained analysis of some reduction games, which characterise various natural subclasses of the first Baire class of functions ranging from and into 0-dimensional Polish spaces, gets new proof of the Baire's lemma on pointwise convergence. Expand
Game representations of classes of piecewise definable functions
  • L. Ros
  • Mathematics, Computer Science
  • Math. Log. Q.
  • 2011
A general way of defining various reduction games on ω which “represent” corresponding topologically defined classes of functions to be useful as a combinatorial tool for the study of general reducibilities for subsets of the Baire space. Expand
  • V. Kiss
  • Mathematics, Computer Science
  • The Journal of Symbolic Logic
  • 2020
This work generalizes Duparc's result by defining a game for an arbitrary function f : X → Y between arbitrary Polish spaces such that Player II has a winning strategy in this game iff f is of Baire class 1. Expand
Games for Functions: Baire Classes, Weihrauch Degrees, Transfinite Computations, and Ranks
  • H. Nobrega
  • Computer Science, Mathematics
  • The Bulletin of Symbolic Logic
  • 2019
Modifications of Semmes's game characterization of the Borel functions are defined, obtaining game characterizations of the Baire class $\alpha$ functions for each fixed $\alpha < \omega_1$. Expand
Some remarks on Baire’s grand theorem
We provide a game theoretical proof of the fact that if f is a function from a zero-dimensional Polish space to $$ \mathbb N^{\mathbb N}$$NN that has a point of continuity when restricted to anyExpand
The Story of a Topological Game
In the author’s dissertation, he introduced a simple topological game. Seemingly minor variations of this game have over the years seen various uses, including the characterization of Corson andExpand
How can we recover Baire class one functions
Let X and Y be separable metrizable spaces, and f:X-->Y be a function. We want to recover f from its values on a small set via a simple algorithm. We show that this is possible if f is Baire classExpand
A minicourse on topological games
Abstract The purpose of these notes is to introduce the basics of topological games and some of the techniques used in the field to the uninitiated reader. We deal mostly with games involvingExpand
Infinite games and generalizations of first-countable spaces
Abstract In this paper we introduce a new class of spaces, called W-spaces, which is defined in terms of a simple two-person infinite game. Every first-countable space is a W-space, and every W-spaceExpand
A survey on topological games and their applications in analysis
Abstract. In this survey article we shall summarise some of the recent progress that has occurred in the study of topological games as well as their applications to abstract analysis. The topicsExpand