Related papers: Baire property of some function spaces

A topological space $X$ is Baire if the intersection of any sequence of open dense subsets of $X$ is dense in $X$. Let $C_p(X,[0,1])$ denote the space of all continuous $[0,1]$-valued functions on a Tychonoff space $X$ with the topology of…

A topological space $X$ is Baire if the Baire Category Theorem holds for $X$, i.e., the intersection of any sequence of open dense subsets of $X$ is dense in $X$. One of the interesting problems in the theory of functional spaces is the…

A topological space $X$ is Baire if the intersection of any sequence of open dense subsets of $X$ is dense in $X$. One of the interesting problems for the space of Baire functions is the Banakh-Gabriyelyan problem: Let $\alpha$ be a…

A topological space $X$ is Baire if the Baire Category Theorem holds for $X$, i.e., the intersection of any sequence of open dense subsets of $X$ is dense in $X$. One of the interesting problems for the space $B_1(X)$ of all Baire-one…

We prove that for a stratifiable scattered space $X$ of finite scattered height, the function space $C_k(X)$ endowed with the compact-open topology is Baire if and only if $X$ has the Moving Off Property of Gruenhage and Ma. As a byproduct…

A topological space $X$ is Baire if the Baire Category Theorem holds for $X$, i.e., the intersection of any sequence of open dense subsets of $X$ is dense in $X$. In this paper, we have obtained that the space $B^{st}_1(X)$ of pointwise…

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…

Let $Y$ be a metrizable space containing at least two points, and let $X$ be a $Y_{\mathcal{I}}$-Tychonoff space for some ideal $\mathcal{I}$ of compact sets of $X$. Denote by $C_{\mathcal{I}}(X,Y)$ the space of continuous functions from…

Let $X$ be a locally compact topological space, $(Y,d)$ be a boundedly compact metric space and $LB(X,Y)$ be the space of all locally bounded functions from $X$ to $Y$. We characterize compact sets in $LB(X,Y)$ equipped with the topology of…

We prove that every homogeneous countable dense homogeneous topological space containing a copy of the Cantor set is a Baire space. In particular, every countable dense homogeneous topological vector space is a Baire space. It follows that,…

A topological space $X$ is Baire if the intersection of any sequence of open dense subsets of $X$ is dense in $X$. We establish that the property $(\kappa)$ for a Tychonoff space $X$ is equivalent to Baireness of $B_1(X)$ and, hence, the…

Burzyk, Kli\'{s} and Lipecki proved that every topological vector space (tvs) $E$ with the property $(K)$ is a Baire space. K\c{a}kol and S\'{a}nchez Ruiz proved that every sequentially complete Fr\'{e}chet--Urysohn locally convex space…

We investigate the Baire classification of mappings $f:X\times Y\to Z$, where $X$ belongs to a wide class of spaces, which includes all metrizable spaces, $Y$ is a topological space, $Z$ is an equiconnected space, which are continuous in…

For a Tychonoff space $X$ and a subspace $Y\subset\mathbb R$, we study Baire category properties of the space $C_{\downarrow F}(X,Y)$ of continuous functions from $X$ to $Y$, endowed with the Fell hypograph topology. We characterize pairs…

We prove some consistency results concerning the Moving Off Property for locally compact spaces and thus the question of whether their function spaces are Baire.

For a Tychonoff space $X$, $B_1(X)$ denotes the space of all Baire-one functions on $X$ endowed with the pointwise topology. We prove that the following assertions are equivalent: (1) $B_1(X)$ is a (semi-)Montel space, (2) $B_1(X)$ is a…

We prove that if $X$ is a paracompact space, $Y$ is a metric space and $f:X\to Y$ is a functionally fragmented map, then (i) $f$ is $\sigma$-discrete and functionally $F_\sigma$-measurable; (ii) $f$ is a Baire-one function, if $Y$ is weak…

A topological space $Y$ has the property (B) of Banakh if there is a countable family $\{A_n:n\in \mathbb{N}\}$ of closed nowhere dense subsets of $Y$ absorbing all compact subsets of $Y$. In this note we show that the space $C_p(X)$ of…

A topological space $X$ is called Piotrowski if every quasicontinuous map $f:Z\to X$ from a Baire space $Z$ to $X$ has a continuity point. In this paper we survey known results on Piotrowski spaces and investigate the relation of Piotrowski…

We present several known and new results on the Baire category properties in topological groups. In particular, we prove that a Baire topological group $X$ is metrizable if and only if $X$ is point-cosmic if and only if $X$ is a…