Related papers: Coding Polish spaces

We study Polish spaces for which a set of possible distances $A \subseteq \mathbb{R}^+$ is fixed in advance. We determine, depending on the properties of $A$, the complexity of the collection of all Polish metric spaces with distances in…

The well known ideal presentations of countably based domains were recently extended to (effective) quasi-Polish spaces. Continuing these investigations, we explore some classes of effective quasi-Polish spaces. In particular, we prove an…

We investigate the effectivizations of several equivalent definitions of quasi-Polish spaces and study which characterizations hold effectively. Being a computable effectively open image of the Baire space is a robust notion that admits…

Following the work of Friedman, Koerwien, Nies and Schlicht we positively answer their question whether the Scott rank of Polish metric spaces is countable.

We introduce the notion of compactifiable classes -- these are classes of metrizable compact spaces that can be up to homeomorphic copies ``disjointly combined'' into one metrizable compact space. This is witnessed by so-called compact…

We propose and study a new approach to the topologization of spaces of (possibly not all) future-directed causal curves in a stably causal spacetime. It relies on parametrizing the curves "in accordance" with a chosen time function. Thus…

We analyse logic actions of Polish groups which arise in continuous logic. We extend the generalised model theory of H.Becker to the case of Polish G-spaces when G is an arbitrary Polish group.

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 characterize coset spaces of topological groups which are coset spaces of (separable) metrizable groups and complete metrizable (Polish) groups. Besides, it is shown that for a $G$-space $X$ with a $d$-open action there is a topological…

We study the usual notion of Scott rank but in the setting of Polish metric spaces. The signature consists of distance relations: for each rational $q > 0$, there is a relation $R_{<q}(x,y)$ stating that the distance of $x$ and $y $ is less…

We investigate computable metrizability of Polish spaces up to homeomorphism. In this paper we focus on Stone spaces. We use Stone duality to construct the first known example of a computable topological Polish space not homeomorphic to any…

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,…

We show that a set of non-negative reals is the distance set of a separable complete metric space if and only if it is either countable or is an analytic set which has 0 as a limit point. We also consider spaces with simpler distance sets.

A topological space is almost locally compact if it contains a dense locally compact subspace. We generalize a result from \cite{Ma}, showing that isomorphism on Borel classes of almost locally compact Polish metric structures is always…

We analyze the effective content of countable, second countable topological spaces by directly calculating the complexity of several topologically defined index sets. We focus on the separation principles, calibrating an arithmetic…

We will characterise robust monetary utility functions defined on the space of real valued (bounded) continuous functions on a Polish space.

We show a necessary and sufficient condition for any ordinal number to be a Polish space. We also prove that for each countable Polish space, there exists a countable ordinal number that is an upper bound for the first component of the…

In this article we extend the notion of metric measure spaces to so-called metric two-level measure spaces (m2m spaces): An m2m space $(X, r, \nu)$ is a Polish metric space $(X, r)$ equipped with a two-level measure $\nu \in…

We will see how to define the metric $\beta$, which turns the topological space of continuous functions whose domains are open subsets of a locally compact and second countable space $X$ to values in a polish space $Y$, called…

Building on our prior work on axiomatization of exact real computation by formalizing nondeterministic first-order partial computations over real and complex numbers in a constructive dependent type theory, we present a framework for…