A5065122943- Advanced Topology and Set Theory
- Rings, Modules, and Algebras
- semigroups and automata theory
- Mathematical Dynamics and Fractals
- Algebraic and Geometric Analysis
- Quasicrystal Structures and Properties
- Limits and Structures in Graph Theory
- Advanced Banach Space Theory
- Homotopy and Cohomology in Algebraic Topology
- Advanced Mathematical Theories and Applications
Eötvös Loránd University
2002-2024
Motivated by a question of Gruenhage, we investigate when $\mathbb R$ is the union less than continuum many translates compact set $C \subseteq \mathbb R$. It will follow from one our general results that if $C$ has packing dimension 1, then not $C$.
Abstract We study generic properties of topological groups in the sense Baire category. First, we investigate countably infinite groups. extend a classical result B. H. Neumann, Simmons and A. Macintyre on algebraically closed word problem. Recently, I. Goldbring, S. Kunnawalkam Elayavalli, Y. Lodha proved that every isomorphism class is meager among In contrast, it follows from work W. Hodges model-theoretic forcing there exists comeager abelian present new elementary proof this result....
This article shines new light on the classical problem of tiling rectangles with squares efficiently a novel method. With twist traditional approach resistor networks, we provide and improved results matter using theory Diophantine Approximation, hence overcoming long-established difficulties, such as generalizations to higher-dimensional analogues. The universality method is demonstrated through its applications different problems. These include other rectangles, their respective...
It is known that the sets of extreme and exposed points a convex Borel subset $\mathbb {R}^n$ are Borel. We show for $n\ge 4$ there exist $G_{\delta }$ subsets such their coincide arbitrarily high class. On other hand, we set $C\subset \mathbb {R}^3$ additive class $\alpha$ ambiguous $\alpha +1$. For proving latter-mentioned results union open closed segments $C\cap \partial C$ if $\alpha$.