Related papers: Locally Contractive Maps on Perfect Polish Ultrame…
On a smooth connected manifold, we consider all possible locally elliptic and locally bounded measurable coefficient Riemannian metrics called rough Riemannian metrics. We equip this set with an extended metric which is connected if and…
A subset of a Polish space $X$ is called universally small if it belongs to each ccc $\sigma$-ideal with Borel base on $X$. Under CH in each uncountable Abelian Polish group $G$ we construct a universally small subset $A_0\subset G$ such…
For random compositions of independent and identically distributed measurable maps on a Polish space, we study the existence and finitude of absolutely continuous ergodic stationary probability measures (which are, in particular, physical…
Analytic self-maps of the unit disc whose hyperbolic derivative is uniformly bounded by a constant smaller than one, are called contractive. We describe these maps in terms of their Aleksandrov-Clark measures and in terms of their…
In this article, we introduce a new type of mapping contracting perimeters of triangles in a complete metric space and present related fixed point theorem. We study the metric completeness property of the underlying space in terms of fixed…
In this paper, we give a characterization of compact sets in $L^p$-spaces on metric measure spaces, which is a generalization of the Kolmogorov-Riesz theorem. Using the criterion, we investigate the topological type of the space consisting…
We prove that if K is a remainder of the Hilbert space (i.e., K is the complement of the Hilbert space in its metrizable compactification) then every non-one-point closed image of K either contains a compact set with no transfinite…
Some fixed point results are given for a class of functional contractions acting on (reflexive) triangular symmetric spaces. Technical connections with the corresponding theories over (standard) metric and partial metric spaces are also…
We develop a stability theory for contractive local IFSs on compact metric spaces. Unlike the classical global setting, local systems may exhibit a richer symbolic and geometric structure, including code spaces that are not of finite type…
This work is motivated by the problem of finding locally compact group topologies for piecewise full groups (a.k.a.~ topological full groups). We determine that any piecewise full group that is locally compact in the compact-open topology…
We prove some "universality" results for topological dynamical systems. In particular, we show that for any continuous self-map $T$ of a perfect Polish space, one can find a dense, $T$-invariant set homeomorphic to the Baire space ${\mathbb…
We introduce the notion of a logarithmic stable map from a minimal log prestable curve to a log twisted semi-stable variety of form $xy=0$. We study the compactification of the moduli spaces of such maps and provide a perfect obstruction…
Uniformly star superparacompactness, which is a topological property between compactness and completeness, can be characterized using finite-component covers and a measure of strong local compactness. Using these finite-component covers and…
We show some basic results on the characterization of quasi-Polish spaces in terms of spaces of ideals, with an emphasis on the connections with computable topology.
We show that the strong operator topology, the weak operator topology and the compact-open topology agree on the space of unitary operators of a infinite dimensional separable Hilbert space. Moreover, we show that the unitary group endowed…
For a compact space $K$ we denote by $C_w(K)$ ($C_p(K)$) the space of continuous real-valued functions on $K$ endowed with the weak (pointwise) topology. In this paper we address the following basic question which seems to be open: Suppose…
We deal with Orlicz-Sobolev embeddings in open subsets of $\mathbb{R}^n$. A necessary and sufficient condition is established for the existence of an optimal, i.e. largest possible, Orlicz-Sobolev space continuously embedded into a given…
Given a class C of subgroups of a topological group G, we say that a subgroup H in C is a universal C subgroup of G if every subgroup K in C is a continuous homomorphic preimage of H. Such subgroups may be regarded as complete members of C…
We prove that the countable product of supercomplete spaces having a countable closed cover consisting of partition-complete subspaces is supercomplete with respect to its metric-fine coreflection. Thus, countable products of…
We prove that if the universal minimal flow of a Polish group $G$ is metrizable and contains a $G_\delta$ orbit $G \cdot x_0$, then it is isomorphic to the completion of the homogeneous space $G/G_{x_0}$ and show how this result translates…