ﻻ يوجد ملخص باللغة العربية
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 similar ideas, we give game characterizations of Baire measurable and Lebesgue measurable functions.
We provide conceptual proofs of the two most fundamental theorems concerning topological games and open covers: Hurewiczs Theorem concerning the Menger game, and Pawlikowskis Theorem concerning the Rothberger game.
Let $fcolonmathbb{R}^2tomathbb{R}$. The notions of feebly continuity and very feebly continuity of $f$ at a point $langle x,yrangleinmathbb{R}^2$ were considered by I. Leader in 2009. We study properties of the sets $FC(f)$ (respectively, $VFC(f)sups
A function $f:Xto Y$ between topological spaces is called $sigma$-$continuous$ (resp. $barsigma$-$continuous$) if there exists a (closed) cover ${X_n}_{ninomega}$ of $X$ such that for every $ninomega$ the restriction $f{restriction}X_n$ is continuous
Families of hypersurfaces that are level-set families of harmonic functions free of critical points are characterized by a local differential-geometric condition. Harmonic functions with a specified level-set family are constructed from geometric dat
We provide a characterization of the set of real-valued functions that can be the value function of some polynomial game. Specifically, we prove that a function $u : dR to dR$ is the value function of some polynomial game if and only if $u$ is a continuous piecewise rational function.