Related papers: A note on Automatic Baire property
We consider the preservation of the properties of automaticity and prefix-automaticity in Rees matrix semigroups over semigroupoids and small categories. Some of our results are new or improve upon existing results in the single-object case…
Abstract numeration systems encode natural numbers using radix ordered words of an infinite regular language and linear recurrence sequences play a key role in their valuation. Sequence automata, which are deterministic finite automata with…
It is known that the family of power means tends to maximum pointwise if we pass argument to infinity. We will give some necessary and sufficient condition for the family of quasi-arithmetic means generated by a functions satisfying certain…
We present a wide class of reflexive, precompact, non-compact, Abelian topological groups $G$ determined by three requirements. They must have the Baire property, satisfy the \textit{open refinement condition}, and contain no infinite…
In the paper we provide new conditions ensuring the isolated calmness property and the Aubin property of parameterized variational systems with constraints depending, apart from the parameter, also on the solution itself. Such systems…
We have defined almost separable space. We show that like separability, almost separability is $c$ productive and converse also true under some restrictions. We establish a Baire Category theorem like result in Hausdorff, Pseudocompacts…
In this book i treat linear algebra over division ring. A system of linear equations over a division ring has properties similar to properties of a system of linear equations over a field. However, noncommutativity of a product creates a…
In this article we give necessary and sufficient conditions that a complex number must satisfy to be a continuous eigenvalue of a minimal Cantor system. Similarly, for minimal Cantor systems of finite rank, we provide necessary and…
We consider systems composed of an unbounded number of uniformly designed linear hybrid automata, whose dynamic behavior is determined by their relation to neighboring systems. We present a class of such systems and a class of safety…
With the help of semi-neighborhoods of the diagonal, classes of Baire spaces are defined: $\Delta$, $\Delta_h$ and $\Delta_s$ Baire spaces. These classes of spaces are studied with the help of topological games. They are useful in studying…
We define the Augmentation property for binary matrices with respect to different rank functions. A matrix $A$ has the Augmentation property for a given rank function, if for any subset of column vectors $x_1,...,x_t$ for for which the rank…
A tree automatic structure is a structure whose domain can be encoded by a regular tree language such that each relation is recognisable by a finite automaton processing tuples of trees synchronously. Words can be regarded as specific…
A simple relation of the order of $n$ abstract objects generates an $n-2$ dimensional basis of three dimensional vectors. A cellular automaton-like model of evolution of this system is postulated. During this evolution, some quantities…
We investigate Baire classes of strongly affine mappings with values in Fr\'echet spaces. We show, in particular, that the validity of the vector-valued Mokobodzki's result on affine functions of the first Baire class is related to the…
Let $\ee>0$ and $\fff$ be a family of finite subsets of the Cantor set $\ccc$. Following D. H. Fremlin, we say that $\fff$ is $\ee$-filling over $\ccc$ if $\fff$ is hereditary and for every $F\subseteq\ccc$ finite there exists $G\subseteq…
We study the automorphism group Aut(G) of a free product G of finite cyclic groups. We investigate the question in which cases Aut(G) has Serre's property FA. In the case of two or three free factors, we prove that Aut(G) does not have…
The inner alignment problem, which asserts whether an arbitrary artificial intelligence (AI) model satisfices a non-trivial alignment function of its outputs given its inputs, is undecidable. This is rigorously proved by Rice's theorem,…
Let $X$ be a compact metrizable space, and let $\Delta$ be a closed set of Borel probability measures on $X$. We study the small boundary property of the pair $(X, \Delta)$. In particular, it is shown that $(X, \Delta)$ has the small…
We provide a detailed study of two properties of spaces and pairs of spaces, the surjection property and the epsilon-surjection property, that were recently introduced to characterize the notion of computable type arising from computability…
This paper introduces abstractions that are meaningful for computers and that can be built and used according to computers' own criteria, i.e., computable abstractions. It is analyzed how abstractions can be seen to serve as the building…