Related papers: On some properties of the space of upper semiconti…
In this paper, we give necessary and sufficient conditions for the space B_1(X) of first Baire class functions on a Tychonoff space X, with pointwise topology, to be (strongly) sequentially separable.
For a Tychonoff space $X$, we denote by $C_k(X)$ the space of all real-valued continuous functions on X with the compact-open topology. In this paper, we have gave characterization for $C_k(X)$ to satisfy $S_{fin}(S, S)$.
For a Tychonoff space X, we denote by B(X) the space of all Baire functions on X with the topology of pointwise convergence. In this paper we investigate selectors for sequences of countable dense and countable sequentially dense sets of…
A separable space is strongly sequentially separable if, for each countable dense set, every point in the space is a limit of a sequence from the dense set. We consider this and related properties, for the spaces of continous and Borel…
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…
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…
We study strongly separately continuous real-valued function defined on the Banach spaces $\ell_p$. Determining sets for the class of strongly separately continuous functions on $\ell_p$ are characterized. We prove that for every $1\le…
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…
For a Tychonoff space $X$, we denote by $C_p(X)$ the space of all real-valued continuous functions on $X$ with the topology of pointwise convergence. We give the functional characterization of the covering property of Hurewicz.
We investigate strongly separately continuous functions on a product of topological spaces and prove that if $X$ is a countable product of real lines, then there exists a strongly separately continuous function $f:X\to\mathbb R$ which is…
Let $USC^*_p(X)$ be the topological space of real upper semicontinuous bounded functions defined on $X$ with the subspace topology of the product topology on ${}^X\mathbb{R}$. $\tilde\Phi^{\uparrow},\tilde\Psi^{\uparrow}$ are the sets of…
For a Tychonoff space $X$, we denote by $(C(X), \tau_k, \tau_p)$ the bitopological space of all real-valued continuous functions on $X$ where $\tau_k$ is the compact-open topology and $\tau_p$ is the topology of pointwise convergence. In…
We give a characterization of the $\Delta_1$-property of any Tychonoff space $X$ in terms of the function space $B_1(X)$ of all Baire-one real-valued functions on a space $X$ with the topology of pointwise convergence. We establish that for…
We prove that the locally convex space $C_{p}(X)$ of continuous real-valued functions on a Tychonoff space $X$ equipped with the topology of pointwise convergence is distinguished if and only if $X$ is a $\Delta$-space in the sense of \cite…
A space $X$ is sequentially separable if there is a countable $S\subset X$ such that every point of $X$ is the limit of a sequence of points from $S$. In 2004, N.V. Velichko defined and investigated concepts close to sequentially…
A Tychonoff space $X$ is called ({\em sequentially}) {\em Ascoli} if every compact subset (resp. convergent sequence) of $C_k(X)$ is equicontinuous, where $C_k(X)$ denotes the space of all real-valued continuous functions on $X$ endowed…
We characterise Tychonoff spaces X so that C(X) is universally {\sigma}-complete and universally complete, respectively.
In paper we study relationships between covering properties of a topological space $X$ and the space $(USC^*(X),\tau_{\mathcal{B}})$ of bounded upper semicontinuous functions on $X$ with the topology $\tau_{\mathcal{B}}$ defined by the…
A classical theorem of Hurewicz characterizes spaces with the Hurewicz covering property as those having bounded continuous images in the Baire space. We give a similar characterization for spaces X which have the Hurewicz property…
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…