相关论文: Topological Study of Pairs of Algebraically Closed…

For a variety over certain topological rings $R$, like $\mathbb{Z}_p$ or $\mathbb{C}$, there is a well-studied way to topologize the $R$-points on the variety. In this paper, we generalize this definition to algebraic stacks. For an…

Let $T$ be a theory which is t-minimal, meaning that with respect to some definable topology, a unary definable set $D \subseteq M$ has non-empty interior iff it is infinite. If $K$ is a definable field in $T$, then $K$ is finite or "large"…

In this paper we have shown that a double sequence in a topological space satisfies certain conditions which in turn are capable to generate a topology on a non empty set. Also we have used the idea of I-convergence of double sequences to…

In many instances in first order logic or computable algebra, classical theorems show that many problems are undecidable for general structures, but become decidable if some rigidity is imposed on the structure. For example, the set of…

We continue work on the topology obtained by the convergence $\lambda_{ls}$, which started in \cite{KuPaCZ}, and further investigated in \cite{KuPaFil19}. The main goal is to describe the closed sets and closure operator by the family of…

We survey some results on the structure of the groups which are definable in theories of fields involved in the applications of model theory to Diophantine geometry. We focus more particularly on separably closed fields of finite degree of…

Let $L$ and $M$ be two algebraically closed fields contained in some common larger field. It is obvious that the intersection $C=L\cap M$ is also algebraically closed. Although the compositum $LM$ is obviously perfect, there is no reason…

Topologies can be expanded with the help of ideals, using the local function, an operator resembling the closure of a set. The aim of this paper is to define the ideals which enable us to create this topology $\tau^{*}$ on $X$…

In algebraic geometry there is the notion of a height pairing of algebraic cycles, which lies at the confluence of arithmetic, Hodge theory and topology. After explaining a motivating example situation, we introduce new directions in this…

In this paper we prove tight bounds on the combinatorial and topological complexity of sets defined in terms of $n$ definable sets belonging to some fixed definable family of sets in an o-minimal structure. This generalizes the…

This paper builds fundamental perfect fields of positive characteristic and shows the structure of perfect fields that a field of positive characteristic is a perfect field if and only if it is an algebraic extension of a fundamental…

A subset of a topological space is constructible if it is a finite Boolean combination of closed sets. We prove that every NTP$_2$ expansion of $(\mathbb{R},<,+)$ by constructible sets defines only constructible sets, and that definable…

Without assuming the field structure on the additive group of real numbers $\mathbb{R}$ with the usual order $<,$ we explore the fact that every proper subgroup of $\mathbb{R}$ is either closed or dense. This property of subgroups of the…

The chapter provides an introduction to the basic concepts of Algebraic Topology with an emphasis on motivation from applications in the physical sciences. It finishes with a brief review of computational work in algebraic topology,…

We study a class of tame $\mathcal{L}$-theories $T$ of topological fields and their $\mathcal{L}_\delta$-extension $T_{\delta}^*$ by a generic derivation $\delta$. The topological fields under consideration include henselian valued fields…

We show how the framework of crossed simplicial groups may be used to provide a classification of topological field theories on open cobordism categories defined by reductions of the structure group to a planar Lie group. Such theories are…

Techniques from higher categories and higher-dimensional rewriting are becoming increasingly important for understanding the finer, computational properties of higher algebraic theories that arise, among other fields, in quantum…

This is a survey of various types of Floer theories (both in symplectic geometry and gauge theory) and relations among them.

We study Michael's lower semifinite topology and Fell's topology on the collection of all closed limit subsets of a topological space. Special attention is given to the subfamily of all maximal limit sets.

We consider a semi-algebraic function defined on a closed semi-algebraic set X. We give formulas relating the topology of X to the indices of the critical points of the function and to the topological behavior of the function at infinity.…