Related papers: On the commutativity of the powerspace constructio…

The past years have seen rapid progress in the classification of topological materials. These diagnostical methods are increasingly getting explored in the pertinent context of magnetic structures. We report on a general class of electronic…

The structure of certain types of quasi shift-invariant spaces, which take the form $V(\psi,\mathcal{X}):=\overline{\text{span}}^{L_2}\{\psi(\cdot-x_j):j\in\mathbb{Z}\}$ for a discrete set $\mathcal{X}=(x_j)\subset\mathbb{R}$ is…

We present a comprehensive theory of boundedness properties for Polish groups developed with a main focus on Roelcke precompactness (precompactness of the lower uniformity) and Property (OB) (boundedness of all isometric actions on…

For the moduli space of unmarked convex $\mathbb{RP}^2$ structures on the surface $S_{g,m}$ with negative Euler characteristic, we investigate the subsets of the moduli space defined by the notions like boundedness of projective invariants,…

A topological dynamical system induces two natural systems, one is on the hyperspace and the other one is on the probability space. The connection among some dynamical properties on the original space and on the induced spaces are…

This paper explores the interactions of absolute continuity of the (quasi)norm with the concepts that are fundamental in the theory of rearrangement-invariant (quasi-)Banach function spaces, such as the Luxemburg representation or the…

This paper studies the C-compact-open topology on the set C(X) of all realvalued continuous functions on a Tychonov space X and compares this topology with several well-known and lesser known topologies. We investigate the properties…

We give some basic properties of strongly topologically transitive, supermixing, and hypermixing maps on general topological spaces. Then we present some other results for which our mappings need to be continuous.

The paper deals with the program of determining the complexity of various homeomorphism relations. The homeomorphism relation on compact Polish spaces is known to be reducible to an orbit equivalence relation of a continuous Polish group…

We report on a study of a one-dimensional linear photonic lattice hosting, simultaneously, fundamental and dipolar modes at every site. We show how, thanks to the interaction between the different orbital modes, this minimal model exhibits…

We extend some known results from smooth dynamical systems to the category of Lipschitz homeomorphisms of compact metric spaces. We consider dynamical properties as robust expansiveness and structural stability allowing Lipschitz…

We provide a classification of compact quantum groups, which can be obtained by the Woronowicz construction, when the arrays used in the twisted determinant condition are extensions of functions on permutations. General properties of such…

The Robnik billiard is investigated in detail both classically and quantally in the transition range from integrable to almost chaotic system. We find out that a remarkable correspondence between characteristic features of classical…

In this paper we present general techniques for characterising minimal and maximal semigroup topologies on the endomorphism monoid $\operatorname{End}(\mathbb{A})$ of a countable relational structure $\mathbb{A}$. As applications, we show…

In this paper we consider composition operators on locally convex spaces of functions defined on $\mathbb{R}$. We prove results concerning supercyclicity, power boundedness, mean ergodicity and convergence of the iterates in the strong…

We associate to every action of a Polish group on a standard probability space a Polish group that we call the orbit full group. For discrete groups, we recover the well-known full groups of pmp equivalence relations equipped with the…

Topology may be interpreted as the study of verifiability, where opens correspond to semi-decidable properties. In this paper we make a distinction between verifiable properties themselves and processes which carry out the verification…

We suggest a new mean field method for studying the thermodynamic competition between magnetic and superconducting phases in a two-dimensional square lattice. A partition function is constructed by writing microscopic interactions that…

We study Zariski-like topologies on a proper class $X\varsubsetneqq L$ of a complete lattice $\mathcal{L}=(L,\wedge ,\vee ,0,1)$. We consider $X$ with the so called classical Zariski topology $(X,\tau ^{cl})$ and study its topological…

We study the structure of the backward shift invariant and nearly invariant subspaces in weighted Fock-type spaces $\mathcal{F}_W^p$, whose weight $W$ is not necessarily radial. We show that in the spaces $\mathcal{F}_W^p$ which contain the…