Related papers: Introduction to Kundt spaces
Recently, the theory of symmetric spaces has come to play an increased role in the physics of integrable systems and in quantum transport problems. In addition, it provides a classification of random matrix theories. In this paper we give a…
Kundt spacetimes are of great importance to General Relativity. We show that a Kundt spacetime is a Lorentz manifold with a non-singular isotropic geodesic vector field having its orthogonal distribution integrable and determining a totally…
The notion of a coherent space is a nonlinear version of the notion of a complex Euclidean space: The vector space axioms are dropped while the notion of inner product is kept. Coherent spaces provide a setting for the study of geometry in…
Some examples and basic properties of ultrametric spaces are briefly discussed.
These informal notes deal with some basic properties of metric spaces, especially concerning lengths of curves.
The paper gives a categorical approach to generalized manifolds such as orbit spaces and leaf spaces of foliations. It is suggested to consider these spaces as sets equipped with some additional structure which generalizes the notion of…
In this paper, we present a constructive generalization of metric and uniform spaces by introducing a new class of spaces, called cover spaces. These spaces form a topological concrete category with a full reflective subcategory of complete…
The goal is to review the notion of a complete Segal space and how certain categorical notions behave in this context. In particular, we study functoriality in complete Segal spaces via fibrations. Then we use it to define limits and…
These notes are an introduction to the theory of quantum symmetries of finite and infinite sets, graphs, and locally compact spaces.
This paper gives a short introduction into the metric theory of spaces with dilations.
Lindel\"of spaces are studied in any basic Topology course. However, there are other interesting covering properties with similar behaviour, such as almost Lindel\"of, weakly Lindel\"of, and quasi-Lindel\"of, that have been considered in…
In this paper, we introduce round and sleek topological spaces and study their properties.
Metric spaces are a fundamental component of mathematics and have a paramount importance as a framework for measuring distance. They can be found in many different branches of mathematics, such as analysis and topology. This paper offers an…
This is a short introduction to affine and convex spaces, written especially for physics students. It summarizes different elementary presentations available in the mathematical literature, and blends analytic- and geometric-flavoured…
An introduction to moduli spaces of representations of quivers is given, and results on their global geometric properties are surveyed. In particular, the geometric approach to the problem of classification of quiver representations is…
In order to provide a good categorical setting to the many different spaces of fields arising in the description of physical theories, a pedagogical introduction to the categorical notion of smooth sets is provided and some simple…
The aim of this paper is to introduce the concept of Delta-Compact spaces along with some basic properties of it. Here, we try to establish the behavior of Delta-Compact spaces under the continuous mapping. Finally, we define another…
The aim of this short lecture series is to expose the students to the beautiful theory of lattices by, on one hand, demonstrating various basic ideas that appear in this theory and, on the other hand, formulating some of the celebrated…
This short note has been written as an Oberwolfach report for the workshop "Differentialgeometrie im Grossen". We discuss properties of metric spaces that at almost all points admit a tangent metric space. We explain why, under some mild…
An introductory overview of vector spaces, algebras, and linear geometries over an arbitrary commutative field is given. Quotient spaces are emphasized and used in constructing the exterior and the symmetric algebras of a vector space.…