On the family of sets of approximate limit numbers
On the statistical and σ-cores
In [11] and [7], the concepts of σ-core and statistical core of a bounded number sequence x have been introduced and also some inequalities which are analogues of Knopp’s core theorem have been proved. In this paper, we characterize the matrices of the class and determine necessary and sufficient conditions for a matrix A to satisfy σ-core(Ax) ⊆ st-core(x) for all x ∈ m.
Pathological functions on Puiseux series ordered fields and others.
-sequence and applications.
Regarding arc-wise accessibility in the plane
Some problems about the limit of a real-valued function
Sur quelques propriétés des ensembles d'ensembles et leurs applieations à la .limite d'une ensemble variable
Symmetric porosity of symmetric Cantor sets
Tauberian conditions for a general limitable method.
The Hurewicz covering property and slaloms in the Baire space
According to a result of Kočinac and Scheepers, the Hurewicz covering property is equivalent to a somewhat simpler selection property: For each sequence of large open covers of the space one can choose finitely many elements from each cover to obtain a groupable cover of the space. We simplify the characterization further by omitting the need to consider sequences of covers: A set of reals X has the Hurewicz property if, and only if, each large open cover of X contains a groupable subcover. This...
The regularity properties on the real line
Two constructions of the real numbers via alternating series.
Ueber eine eigenthümliche Bestimmung einer Function durch formale Anforderungen.
Ueber einige Punkte der Functionentheorie.
Uncountable γ-sets under axiom
We formulate a Covering Property Axiom , which holds in the iterated perfect set model, and show that it implies the existence of uncountable strong γ-sets in ℝ (which are strongly meager) as well as uncountable γ-sets in ℝ which are not strongly meager. These sets must be of cardinality ω₁ < , since every γ-set is universally null, while implies that every universally null has cardinality less than = ω₂. We also show that implies the existence of a partition of ℝ into ω₁ null compact sets....
Very slowly varying functions. II
This paper is a sequel to papers by Ash, Erdős and Rubel, on very slowly varying functions, and by Bingham and Ostaszewski, on foundations of regular variation. We show that generalizations of the Ash-Erdős-Rubel approach-imposing growth restrictions on the function h, rather than regularity conditions such as measurability or the Baire property-lead naturally to the main result of regular variation, the Uniform Convergence Theorem.
Věta o supremu a věty s ní ekvivalentní
Základové arithmetiky. [I.]
О кoнcтpуктивнпм aналоге тeopeмы Дaнжуa-Янгa о пpoизводных чиcлax
О кoнcтpуктивныx пceвдочиcлax