Related papers: On the pointwise limits of sequences of \'Swi\k{a}…
We obtain a pointwise description of functions belonging to function spaces with the lattice property. In particular, it is valid for Banach function spaces provided that the Hardy-Littlewood maximal operator is bounded. We also study…
We give a topological characterization of the n-dimensional pseudo-boundary of the (2n+1)-dimensional Euclidean space.
In this paper we study the number of finite topologies on an $n$-element set subject to various restrictions.
Abstrct: In this note, by considering fractionally linear functions over a finite field and consequently developing an abstract sequence, we study some of its properties.
We study some important topological properties such as boundedness, compactness and essential norm of differences of weighted composition operators between Fock spaces
This paper catalogues a variety of examples concerning a type of function of a $p$-adic integer variable defined by a formal series expression we have dubbed "$\mathcal{F}$-series". These series exhibit a new, previously undocumented form…
The $S$ topology on the Skorokhod space was introduced by the author in 1997 and since then it proved to be a useful tool in several areas of the theory of stochastic processes. The paper brings complementary information on the $S$…
For some self-similar sets K in d-dimensional Euclidean space we obtain certain lower bounds for the lower Minkowski dimension of K+E in terms of the lower Minkowski dimension of E.
We establish simple pointwise characterizations of functions in the Hardy-Sobolev spaces within the range n/(n+1)<p <=1. In addition, classical Hardy inequalities are extended to the case p <= 1.
We review the theory of splittings of hyperbolic groups, as determined by the topology of the boundary. We give explicit examples of certain phenomena and then use this to describe limit sets of Kleinian groups up to homeomorphism.
On any metric space, I provide an intrinsic characterization of those complex-valued functions which are uniform limits of Lipschitz functions. There are applications to function theory on complete Riemannian manifolds and, in particular,…
The Minkowski functionals are a mathematical tool to quantify morphological features of patterns. Some applications to the matter distribution in galaxy catalogues and N-body simulations are reviewed, with an emphasis on the effects of…
We discuss some results concerning fixed point equations in the setting of topological *-algebras of unbounded operators. In particular, an existence result is obtained for what we have called {\em weak $\tau$ strict contractions}, and some…
We study tightness properties and selective versions of separability in bitopological function spaces endowed with set-open topologies.
The properties of the spaces of Sugeno integrable functions are quite different from those of the ordinary spaces of Lebesgue integrable functions. The purpose of the paper is to further advance our study of the Sugeno-Lorentz spaces, in…
The Minkowski function is a crucial tool used in the study of balanced domains and, more generally, quasi-balanced domains in several complex variables. If a quasi-balanced domain is bounded and pseudoconvex then it is well-known that its…
Upper semicontinuous (usc) functions arise in the analysis of maximization problems, distributionally robust optimization, and function identification, which includes many problems of nonparametric statistics. We establish that every usc…
A simple parametrization for the octupole collective variables is proposed and the symmetries of the wave functions are discussed in terms of the solutions corresponding to the vibrational limit. [PACS: 21.60Ev, 21.60.Fw, 21.10.Re]
In this article we prove that the singular set of Dirichlet-minimizing $Q$-valued functions is countably $(m-2)$-rectifiable and we give upper bounds for the $(m-2)$-dimensional Minkowski content of the set of singular points with…
This paper treats the variation of sets. We attempt to formulate convergence and continuity of set-valued functions in a different way from the theories on sequences of sets and correspondence. In the final section, we also attempt to…