Related papers: $L$-Topology via Generalised Geometric Logic
In this Master of Science Thesis I introduce geometric algebra both from the traditional geometric setting of vector spaces, and also from a more combinatorial view which simplifies common relations and operations. This view enables us to…
A number of models of linear logic are based on or closely related to linear algebra, in the sense that morphisms are "matrices" over appropriate coefficient sets. Examples include models based on coherence spaces, finiteness spaces and…
A generic method for combinatorial constructions of intrinsic geometrical spaces is presented. It is based on the well known inverse sequences of finite graphs that determine (in the limit) topological spaces. If a pattern of the…
This paper presents a novel concept of a Polyatomic Logic and initiates its systematic study. This approach, inspired by Inquisitive semantics, is obtained by taking a variant of a given logic, obtained by looking at the fragment covered by…
A broader definition of generalized truncations of graphs is introduced followed by an exploration of some standard concepts and parameters with regard to generalized truncations.
We present a set of principles and methodologies which may serve as foundations of a unifying theory of Mathematics. These principles are based on a new view of Grothendieck toposes as unifying spaces being able to act as `bridges' for…
In this paper, we give a survey of a geometrical theory of Jacobi forms of higher degree. And we present some geometric results and discuss some geometric problems to be investigated in the future.
This paper considers generalizations of open mappings, closed mappings, pseudo-open mappings, and quotient mappings from topological spaces to generalized topological spaces. Characterizations of these classes of mappings are obtained and…
We give a modern account of the construction and structure of the space of generalized connections, an extension of the space of connections that plays a central role in loop quantum gravity.
In this paper we will relate hyperstructures and the general $\mathscr{H}$-principle to known mathematical structures, and also discuss how they may give rise to new mathematical structures. The main purpose is to point out new ideas and…
We introduce relational semantics for "flat Heyting-Lewis logic" $\mathsf{HLC}^{\flat}$. This logic arises as the extension of intuitionistic logic with a Lewis-style strict implication modality that, contrary to its "sharp" counterpart…
We introduce the notion of induced Maslov cycle, which describes and unifies geometrical and topological invariants of many apparently unrelated problems, from Real Algebraic Geometry to sub-Riemannian Geometry.
We set up some foundations of generalised scheme theory related to new incompressible symmetric tensor categories. This is analogous to the relation between super schemes and the category of super vector spaces.
In this paper intuitionistic topological system and its properties have been introduced. Categorical interrelationships among Heyting algebra, G\"odel algebra, Esakia space and proposed intuitionistic topological systems have also been…
We show that unlike the usual topologies the $g$-topologies are closed with respect to the Cartesian products. Moreover, we bring much detailed explanations some examples of concepts related the statistical metric spaces.
A category which generalises to higher dimensions many of the features of the Temperley-Lieb category is introduced.
The weighted triangulation algebras associated to triangulation quivers and their socle deformations were recently introduced and studied in [15]-[20] and [2]. These algebras, based on surface triangulations and originated from the theory…
We discuss the role played by logarithmic structures in the theory of moduli.
This is the first chapter in our "Toric Topology" book project. Further chapters are coming. Comments and suggestions are very welcome.
A new methodological approach for the study of topology for shapes made of arrangements of lines, planes or solids is presented. Topologies for shapes are traditionally built on the classical theory of point-sets. In this paper, topologies…