Related papers: Problems on $\beta\mathbb{N}$

In [15], V. Jimenez and J. Llibre characterized, up to homeomorphism, the omega limit sets of analytic vector fields on the sphere and the projective plane. The authors also studied the same problem for open subsets of these surfaces.…

We establish diverse relationships between the algorithmic (Kolmogorov) complexity of the prefixes of any binary expansion and $\beta$-expansions. These relationships allow to develop intuitions on the complexity behavior of…

This is a survey recent works on topological extensions of the Tutte polynomial.

Work in progress concerning alternative formalizations of arithmetic.

This paper presents fifteen problems about mapping class groups. It is an expanded and updated version of the author's preprint "Ten problems on the mapping class groups". The paper will appear in the book "Problems on Mapping Class Groups…

In this paper, we presented another concept of N-O.S. called NS{\alpha}-O.S. and studied their fundamental properties in nano topological spaces. We also present NS{\alpha}-interior and NS{\alpha}-closure and study some of their fundamental…

Here we give a reformulation of a key lemma in the paper [2], "Spaces of Topological Complexity One", which is necessary due to an oversight.

We propose a list of open problems in numerical semigroups.

We prove that the pluri-fine topology on any open set $\Omega$ in $\mathbb{C}^{n}$ is locally connected. This answers a question by Fuglede in [4]. See also Bedford [6].

We study two principle minimizing problems, subject of different constraints. Our open sets are assumed bounded, except mentioning otherwise;precisely $\Omega=]0,1[^n \in {\mathbb{R}}^n , n=1 $ or $n=2$.

This is a paper in Analytic Topology.

In this short note we present some remarks and conjectures on two of Erd\"os's open problems in number theory.

A brief survey of some aspects of noetherian Hopf algebras is given, concentrating on structure, homology, and classification, and accompanied by a panoply of open problems.

The purpose of this paper is to continue studying the properties of $\gamma$-regular open sets introduced and explored in [6]. The concept of $\gamma$-closed spaces have also been defined and discussed.

We introduce the concept of linear topological modules over vertex algebras and apply it to representations of $\beta-\gamma$ system and affine Kac-Moody algebras.

Notions of topological free entropy and of free capacity are introduced in the $C^*$-algebra context. Basic properties, basic problems and connections to potential theory and random matrix theory are discussed.

In this paper some open problems for Painlev\'e equations are discussed. In particular the following open problems are described: (i) the Painlev\'e equivalence problem; (ii) notation for solutions of the Painlev\'e equations; (iii)…

It is expected that the $D$-topology makes every diffeological vector space into a topological vector space. We show that it is the case for a large class of diffeological vector spaces via $k_\omega$-space theory, but not so in general.…

We discuss Beta operators with Jacobi weights on $C[0,1]$ for $\alpha,\beta\geq-1$, thus including the discussion of three limiting cases. Emphasis is on the moments and their asymptotic behavior. Extended Voronovskaya-type results and a…

We investigate closed copies of~$\mathbb{N}$ in powers of~$\mathbb{R}$ with respect to $C^*$- and $C$-embedding. We show that $\mathbb{R}^{\omega_1}$ contains closed copies of~$\mathbb{N}$ that are not $C^*$-embedded.