Related papers: Coding Polish spaces
We develop a unified framework for locating natural properties of algebraic and analytic structures within the Borel hierarchy. Objects are presented as quotients of a universal generator and definability is read directly from the quotient…
We construct the space of valuations on a quasi-Polish space in terms of the characterization of quasi-Polish spaces as spaces of ideals of a countable transitive relation. Our construction is closely related to domain theoretical work on…
We introduce strings in metric spaces and define string complexes of metric spaces. We describe the class of 2-dimensional topological spaces which arise in this way from finite metric spaces.
We define some coding of Borel sets in admissible sets. Using this we generalize certain results from model theory involving admissible sets to the case of continuous actions of closed permutation groups on Polish spaces. In particular we…
If $\mathcal{N}$ is a proper Polish metric space and $\mathcal{M}$ is any countable dense submetric space of $\mathcal{N}$, then the Scott rank of $\mathcal{N}$ in the natural first order language of metric spaces is countable and in fact…
A coding method using binary sequences is presented for different computation problems related to Catalan numbers. This method proves in a very easy way the equivalence of these problems.
In this article we studied the relationship between metric spaces and multiplicative metric spaces. Also, we pointed out some fixed and common fixed point results under some contractive conditions in multiplicative metric spaces can be…
We study an extensive connection between factor forcings of Borel subsets of Polish spaces modulo a sigma-ideal, and factor forcings of subsets of countable sets modulo an ideal.
We show that if an equivalence relation $E$ on a Polish space is a countable union of smooth Borel subequivalence relations, then there is either a Borel reduction of $E$ to a countable Borel equivalence relation on a Polish space or a…
A construction is presented that allows to produce subspace codes of long length using subspace codes of shorter length in combination with a rank metric code. The subspace distance of the resulting code, called linkage code, is as good as…
We give, for some Borel sets of a product of two Polish spaces, including the Borel sets with countable sections, a Hurewicz-like characterization of those which cannot become a transfinite difference of open sets by changing the two Polish…
We will show that, consistently, every uncountable set can be continuously mapped onto a non measure zero set, while there exists an uncountable set whose all continuous images into a Polish space are meager.
While there is a well-established notion of what a computable ordinal is, the question which functions on the countable ordinals ought to be computable has received less attention so far. We propose a notion of computability on the space of…
We investigate some basic descriptive set theory for countably based completely quasi-metrizable topological spaces, which we refer to as quasi-Polish spaces. These spaces naturally generalize much of the classical descriptive set theory of…
In algorithms for finite metric spaces, it is common to assume that the distance between two points can be computed in constant time, and complexity bounds are expressed only in terms of the number of points of the metric space. We…
We begin the systematic study of decision problems for finitely generated groups given by a solution to their word problem. We relate this to the study of computable analysis on the space of marked groups. We point out that several distinct…
This study investigates the relationship between the phonological and morphological structure of Polish words and their meanings using Distributional Semantics. In the present analysis, we ask whether there is a relationship between the…
If G is a Polish group, then there is a Polish G-space X which is universal among Polish G-spaces with respect to continuous G-embeddings.
A marked metric measure space (mmm-space) is a triple (X,r,mu), where (X,r) is a complete and separable metric space and mu is a probability measure on XxI for some Polish space I of possible marks. We study the space of all (equivalence…
We investigate conditions under which a co-computably enumerable set in a computable metric space is computable. Using higher-dimensional chains and spherical chains we prove that in each computable metric space which is locally computable…