相关论文: Some notes on spaces of ideals and computable topo…
Represented spaces form the general setting for the study of computability derived from Turing machines. As such, they are the basic entities for endeavors such as computable analysis or computable measure theory. The theory of represented…
We consider the set of all the ideals of a ring, endowed with the coarse lower topology. The aim of this paper is to study the topological properties of distinguished subspaces of this space and detect the spectrality of some of them.
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 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…
These are some informal notes concerning topological vector spaces, with a brief overview of background material and basic notions, and emphasis on examples related to classical analysis.
Almost all representations considered in computable analysis are partial. We provide arguments in favor of total representations (by elements of the Baire space). Total representations make the well known analogy between numberings and…
The concept of quasi-partial b-metric-like spaces is being introduced and studied with the help of topology. Examples are also discussed to support the results. Some fixed point theorems are proved in the setting of quasi-partial…
In this paper, we consider certain topological properties along with certain types of mappings on these spaces defined by the notion of ideal convergence. In order to do that, we primarily follow in the footsteps of the earlier studies of…
We investigate the properties of ideals associated with Kuratowski partitions of non-complete Baire metric spaces. We show that such an ideal can be precipitous.
This article continues the study of computable elementary topology started by the author and T. Grubba in 2009 and extends the author's 2010 study of axioms of computable separation. Several computable T3- and Tychonoff separation axioms…
We consider the isometry group of the infinite dimensional separable hyperbolic space with its Polish topology. This topology is given by the pointwise convergence. For non-locally compact Polish groups, some striking phenomena like…
We study computable topological spaces and semicomputable and computable sets in these spaces. In particular, we investigate conditions under which semicomputable sets are computable. We prove that a semicomputable compact manifold $M$ is…
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…
In a recent paper, two multi-representations for the measurable sets in a computable measure space have been introduced, which prove to be topologically complete w.r.t. certain topological properties. In this contribution, we show them…
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…
Computable analysis and effective descriptive set theory are both concerned with complete metric spaces, functions between them and subsets thereof in an effective setting. The precise relationship of the various definitions used in the two…
We study here the topology of information on the space of probability measures over Polish spaces that was defined in Hellwig (1996). We show that under this topology, a convergent sequence of probability measures satisfying a conditional…
A Polish space is not always homeomorphic to a computably presented Polish space. In this article, we examine degrees of non-computability of presenting homeomorphic copies of compact Polish spaces. We show that there exists a…
A class of Cantor-type spaces and related geometric structures are discussed.
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…