Related papers: Selection Principles and Baire spaces

n infinite two-player zero-sum game with a Borel winning set, in which the opponent's actions are monitored eventually but not necessarily immediately after they are played, is determined. The proof relies on a representation of the game as…

We show that if $X$ and $Y$ are Banach spaces, where $Y$ is separable and polyhedral, and if $T:X \to Y$ is a bounded linear operator such that $T^*(Y^*)$ contains a boundary $B$ of $X$, then $X$ is separable and isomorphic to a polyhedral…

A set of reals $X$ is $\mathfrak{b}$-concentrated if it has cardinality at least $\mathfrak{b}$ and it contains a countable set $D\subseteq X$ such that each closed subset of $X$ disjoint with $D$ has size smaller than $\mathfrak{b}$. We…

Dependence on the parameter is continuous when perturbations of the parameter preserves strict preference for one alternative over another. We characterise this property via a utility function over alternatives that depends continuously on…

This paper deals with a property which is equivalent to generalised-lushness for separable spaces. It thus may be seemed as a geometrical property of a Banach space which ensures the space to have the Mazur-Ulam property. We prove that if a…

We construct Menger subsets of the real line whose product is not Menger in the plane. In contrast to earlier constructions, our approach is purely combinatorial. The set theoretic hypothesis used in our construction is far milder than…

We introduce a property of posets which strengthens (\omega_1+1)-strategic closedness. This property is defined using a variation of the Banach-Mazur game on posets, where the first player chooses a countable set of conditions instead of a…

We extend the Fundamental Theorem of Epistemic Game Theory to games with Baire class one payoffs and locally compact Polish strategy spaces, and under Projective Determinacy, to games with analytically measurable payoffs and arbitrary…

The famous Michael selection theorem deals with the characterisation of paracompact spaces by continuous selections of lower semi-continuous mappings in Banach spaces. In this paper, we will discuss several equivalent forms of this theorem,…

A separable Banach space X contains $\ell_1$ isomorphically if and only if X has a bounded wc_0^*-stable biorthogonal system. The dual of a separable Banach space X fails the Schur property if and only if X has a bounded wc_0^*-biorthogonal…

The purpose of this paper is to define for every Polish space $X$ a class of sets, the $EBP(X)$-sets or the extended Baire property sets, to work out many properties of the $EBP(X)$-sets and to show their usefulness in analysis. For…

We prove the following two results. 1. If $X$ is a completely regular space such that for every topological space $Y$ each separately continuous function $f:X\times Y\to\mathbb R$ is of the first Baire class, then every Lindel\"of subspace…

We study the parameterized complexity of several positional games. Our main result is that Short Generalized Hex is W[1]-complete parameterized by the number of moves. This solves an open problem from Downey and Fellows' influential list of…

Hurewicz proved completely metrizable Menger spaces are /sigma-compact. We extend this to Cech-complete Menger spaces and consistently to projective Menger metrizable spaces. On the other hand, it is consistent that there is a co-analytic…

We study a generalisation of B\"uchi-Landweber games to the timed setting. The winning condition is specified by a non-deterministic timed automaton with epsilon transitions and only Player I can elapse time. We show that for fixed number…

We provide a detailed study of two properties of spaces and pairs of spaces, the surjection property and the epsilon-surjection property, that were recently introduced to characterize the notion of computable type arising from computability…

The classical Banach-Mazur game characterizes sets of first category in a topological space. In this work, we show that an effectivized version of the game yields a characterization of sets of effective first category. Using this, we give a…

Property~(A) is a week symmetry condition that plays a fundamental role in the characterization of greedy-type bases in the isometric case, i.e., when the constants involved in the study of the efficiency of the thresholding greedy…

A Banach space has the ball huskable property ($BHP$) if the closed unit ball has weakly open sets of arbitrarily small diameter. We can analogously define $w^*$-$BHP$ in the dual space. In this short note, we study these properties in the…

We prove that the existence of a Hurewicz fibration between certain spaces with the homotopy type of a CW-complex implies some topological restrictions on their universal coverings. This result is used to deduce differentiable and metric…