Related papers: Topological proofs of results on large fields
We show how to use topological ideas, such as compactness, to establish orderability properties of infinite groups. A new application is to provide a left-ordering for the group of PL homeomorphisms of a connected surface with boundary…
In this paper we introduce a new technique to prove the existence of closed subspaces of maximal dimension inside sets of topological vector sequence spaces. The results we prove cover some sequence spaces not studied before in the context…
Pseudo algebraically closed, pseudo real closed, and pseudo $p$-adically closed fields are examples of unstable fields that share many similarities, but have mostly been studied separately. In this text, we propose a unified framework for…
Recently, Mr\v{s}evi\'{c} and Reilly discussed some covering properties of a topological space and its associated $\alpha$-topology in both topological and bitopological ways. The main aim of this paper is to investigate some common and…
Topological Data Analysis is a recent and fast growing field providing a set of new topological and geometric tools to infer relevant features for possibly complex data. This paper is a brief introduction, through a few selected topics, to…
We develop a sequential-topological study of rational points of schemes of finite type over local rings typical in higher dimensional number theory and algebraic geometry. These rings are certain types of multidimensional complete fields…
We describe a "top down" approach for automated theorem proving (ATP). Researchers might usefully investigate the forms of the theorems mathematicians use in practice, carefully examine how they differ and are proved in practice, and code…
We survey some results on real rational surfaces focused on their topology and their birational geometry.
We provide a simple proof for the union-closed sets conjecture, a long-standing open problem in set theory with immediate applications to graph theory, number theory, and order-theory.
We prove the existence of infinitely many solutions to an elliptic problem by borrowing the techniques from algebraic topology. The solution(s) thus obtained will also be proved to be bounded.
The concept of $typed$ $topology$ is introduced. In a typed topological space, some open sets are assigned "types", and topological concepts such as closure, connectedness can be defined using types. A finite data set in $R^2$ is a…
We introduce an abstract topos-theoretic framework for building Galois-type theories in a variety of different mathematical contexts; such theories are obtained from representations of certain atomic two-valued toposes as toposes of…
We give an exposition of Natural Topology (NToP), which highlights its advantages for exact computation. The NToP-definition of the real numbers (and continuous real functions) matches recent expert recommendations for exact real…
We develop the theory of locally small spaces in a new simple language and apply this simplification to re-build the theory of locally definable spaces over structures with topologies.
This is a review of the fundamental concepts of general topology.
We give a new proof of the Gibbard-Satterthwaite Theorem. We construct two topological spaces: one for the space of preference profiles and another for the space of outcomes. We show that social choice functions induce continuous mappings…
In the recent years, we have linked a large corpus of formal mathematics with automated theorem proving (ATP) tools, and started to develop combined AI/ATP systems working in this setting. In this paper we first relate this project to the…
In this paper we define a topology with sufficiently good properties on the set of prime ideals of a number field.
Covering-based rough set theory is an extension to classical rough set. The main purpose of this paper is to study covering rough sets from a topological point of view. The relationship among upper approximations based on topological spaces…
Using recent results in topos theory, two systems of higher-order logic are shown to be complete with respect to sheaf models over topological spaces---so-called ``topological semantics''. The first is classical higher-order logic, with…