Related papers: Separately continuous functions on products and it…
The purpose of this paper is to study the Sarason's problem on Fock spaces of polyanalytic functions. Namely, given two polyanalytic symbols $f$ and $g$, we establish a necessary and sufficient condition for the boundedness of some Toeplitz…
In this paper, we investigate and find a necessary and sufficient condition for a function to be absolutely continuous over $\mathbb{R}$ (denoted by $AC(\mathbb{R})$) or any unbounded interval in $\mathbb{R}$ . Note that the Lebesgue's…
We prove general results about separation and weak$^\#$-convergence of boundedly finite measures on separable metric spaces and Souslin spaces. More precisely, we consider an algebra of bounded real-valued, or more generally a $*$-algebra…
This paper is concerned with dependence of discrete Sturm-Liouville eigenvalues on problems. Topologies and geometric structures on various spaces of such problems are firstly introduced. Then, relationships between the analytic and…
Let $X,Y$ be topological vector spaces or metric spaces, and let {$f:X\times Y \to \Re $} be a real function lower semicontinuous in the first variable and upper semicontinuous in the second one. It is proved that $f$ is globally…
The minimal and the maximal sections $\wedge_f,\vee\!_f:X\to\overline{\mathbb R}$ of a function $f:X\times Y\to\overline{\mathbb R}$ are defined by $\wedge_f(x)=\inf\limits_{y\in Y}f(x,y)$ and $\vee\!\!_f(x)=\sup\limits_{y\in Y}f(x,y)$ for…
We study product regular conditional probabilities under measures of two coordinates with respect to the second coordinate that are weakly continuous on the support of the marginal of the second coordinate. Assuming that there exists a…
A function $f:X\to Y$ between topological spaces is called {\em compact-preserving} if the image $f(K)$ of each compact subset $K\subset X$ is compact. We prove that a function $f:X\to Y$ defined on a strong Frechet space $X$ is…
We study time- and parameter-dependent ordinary differential equations in the geometric setting of vector fields and their flows. Various degrees of regularities in state are considered, including Lipschitz, finitely diferentiable, smooth,…
We consider approximations of a continuous function on a countable normed Fr\'{e}chet space by analytic and $*$-analytic. Also we found a criterium of the existence of an extension of a continuous function from a dense subspace of a…
We introduce a continuous domain for function spaces over topological spaces which are not core-compact. Notable examples of such topological spaces include the real line with the upper limit topology, which is used in solution of initial…
A map $f:X\to Y$ between topological spaces is defined to be {\em scatteredly continuous} if for each subspace $A\subset X$ the restriction $f|A$ has a point of continuity. We show that for a function $f:X\to Y$ from a perfectly paracompact…
In this paper we provide in $\bFp$ expanding lower bounds for two variables functions $f(x,y)$ in connection with the product set or the sumset. The sum-product problem has been hugely studied in the recent past. A typical result in…
We show that in a metric space, any continuous function with compact sublevel sets and finite metric slope is uniquely determined by the slope and its critical values.
Some new results about multidimensional Topological Persistence are presented, proving that the discontinuity points of a k-dimensional size function are necessarily related to the pseudocritical or special values of the associated…
We construct an example of a real-valued continuous non-constant function $f$ defined on a connected complete metric space $X$ such that every point of $X$ is a point of local minimum or local maximum for $f$. The space $X$ is connected but…
New singularity theorems are derived for generic warped-product spacetimes of any dimension. The main purpose is to analyze the stability of (compact or large) extra dimensions against dynamical perturbations. To that end, the base of the…
We investigate the behavior of functional countability and exponential separability in products and subspaces of topological spaces. We solve a problem of Tkachuk by showing that the product of functionally countable pseudocompact spaces is…
In these notes, uniform convergence on compacta is studied on the space of functions taking values in the set of finite Borel measures. Related limit theorems, including L\'evy's continuity theorem and functional limit theorems for…
We study entire functions whose zeros and one-points lie on distinct finite systems of rays. General restrictions on these rays are obtained. Non-trivial examples of entire functions with zeros and one-points on different rays are…