Related papers: On the commutativity of the powerspace constructio…
In this paper, we study the chaotic dynamics of a continuous-time topological semi-flow on a Polish space.
We study $G_\delta$ subspaces of continuous dcpos, which we call domain-complete spaces, and $G_\delta$ subspaces of locally compact sober spaces, which we call LCS-complete spaces. Those include all locally compact sober spaces-in…
We investigate robust Orlicz spaces as a generalisation of robust $L^p$-spaces. Two constructions of such spaces are distinguished, a top-down approach and a bottom-up approach. We show that separability of robust Orlicz spaces or their…
Here, the composition operators on Orlicz spaces with finite ascent and descent as well as infinite ascent and descent are characterized.
The article is devoted to a structure of topological spaces related with topological quasigroups. Regular and complete spaces over topological quasigroups are studied. Separations and embeddings are also investigated for them. Their…
Powerspaces of directed spaces play an important role in modeling the semantics of nondeterministic functional programming languages. The notions of upper,lower and convex powerspace of a directed space are defined by the way of free…
To understand an aperiodic tiling (or a quasicrystal modeled on an aperiodic tiling), we construct a space of similar tilings, on which the group of translations acts naturally. This space is then an (abstract) dynamical system. Dynamical…
In this paper, we use elementary and simple ideas which are based on the significant applications of the power set ring to rebuild and study the patch topology on the prime spectrum from a completely different and new point of view.…
In this paper we introduce a new kind of topological space, called 'structured space', which locally resembles various kinds of algebraic structures. This can be useful, for instance, to locally study a space that cannot be globally endowed…
We investigate the causal relations in the space of states of almost commutative Lorentzian geometries. We fully describe the causal structure of a simple model based on the algebra $\mathcal{S}(\mathbb{R}^{1,1}) \otimes M_2(\mathbb{C})$,…
The set of increasing functions on the rational numbers, equipped with the composition operation, naturally forms a topological semigroup with respect to the topology of pointwise convergence in which a sequence of increasing functions…
A compact Polish foliated space is considered. Part of this work studies coarsely quasi-isometric invariants of leaves in some residual saturated subset when the foliated space is transitive. In fact, we also use "equi-" versions of this…
We study the topology of a class of proper submodules and some of its distinguished subclasses and call them structure spaces. We give several criteria for the quasi-compactness of these structure spaces. We study $T_0$ and $T_1$ separation…
The aim of this paper is to discuss the characterizations of the composition operators on Orlicz-Lorentz space to have finite ascent (or descent).
In the present paper we provide some equivalent conditions for composition operators to have shadowing property on Orlicz space. Also, we obtain that for the composition operators on Orlicz spaces the notions of generalized hyperbolicity…
We characterize the Hurewicz cofibrations between finite topological spaces, that is, the continuous functions between finite topological spaces that have the homotopy extension property with respect to all topological spaces. In…
We analyze the reducibilities induced by, respectively, uniformly continuous, Lipschitz, and nonexpansive functions on arbitrary ultrametric Polish spaces, and determine whether under suitable set-theoretical assumptions the induced…
In this note, we investigate some topological properties of probabilistic modular spaces.
We define a moduli space of translation structures on the open topological disk with a basepoint and endow it with a locally-compact metrizable topology. We call this the immersive topology, because it is defined using the concept of…
We use Fra\" iss\'e theoretic methods to construct several universal and ultrahomogeneous Polish metric structures. Namely, universal and ultrahomogeneous Polish metric space equipped with countably many closed subsets of its powers,…