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We propose an axiomatic characterization of coarse homology theories defined on the category of bornological coarse spaces. We construct a category of motivic coarse spectra. Our focus is the classification of coarse homology theories and…
For a topological flow $(V,\phi)$ - i.e., $V$ is a linearly compact vector space and $\phi$ a continuous endomorphism of $V$ - we gain a deep understanding of the relationship between $(V,\phi)$ and the Bernoulli shift: a topological flow…
Constructive properties of uniform convexity, strict convexity, near convexity, and metric convexity in real normed linear spaces are considered. Examples show that certain classical theorems, such as the existence of points of osculation,…
We show that all extended functorial field theories, both topological and nontopological, are local. We define the smooth (infinity,d)-category of bordisms with geometric data, such as Riemannian metrics or geometric string structures, and…
The theory of analytic function spaces in very general tubular domains over symmetric cones is a relatively new interesting research area. Tube domains are very general and very complicated domains. Recently several new results in this…
The topology of an object describes global properties that are insensitive to local perturbations. Classic examples include string knots and the genus (number of handles) of a surface: no manipulation of a closed string short of cutting it…
A classical set of birational invariants of a variety are its spaces of pluricanonical forms and some of their canonically defined subspaces. Each of these vector spaces admits a typical metric structure which is also birationally…
We give a self-contained and enriched review about topology properties in the rapidly growing field of topological states of matter (TSM). This review is mainly focus on the beautiful interplay of topology mathematics and condensed matter…
Higher-order probabilistic programming languages allow programmers to write sophisticated models in machine learning and statistics in a succinct and structured way, but step outside the standard measure-theoretic formalization of…
In this article we introduce Variable exponent Fock spaces and study some of their basic properties such as the boundedness of evaluation functionals, density of polynomials, boundedness of a Bergman-type projection and duality.
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…
Homotopy type theory is a new branch of mathematics, based on a recently discovered connection between homotopy theory and type theory, which brings new ideas into the very foundation of mathematics. On the one hand, Voevodsky's subtle and…
A classical theorem of Hurewicz characterizes spaces with the Hurewicz covering property as those having bounded continuous images in the Baire space. We give a similar characterization for spaces X which have the Hurewicz property…
This note presents an extension of a result within the concept of [S]-lineability, originally developed in 2019 by L. Bernal-Gonz\'alez, J.A. Conejero, M. Murillo-Arcila, and J.B. Seoane-Sep\'ulveda . Additionally, we provide a…
In the first part of this paper we discuss the completeness of two general classes of weighted inductive limits of spaces of ultradifferentiable functions. In the second part we study their duals and characterize these spaces in terms of…
Normed spaces appear to have very little going for them: aside from the hackneyed linear structure, you get a norm whose only virtue, aside from separating points, is the Triangle Inequality. What could you possibly prove with that? As it…
We provide a formal introduction into the classic theorems of general topology and its axiomatic foundations in set theory. In this second part we introduce the fundamental concepts of topological spaces, convergence, and continuity, as…
Statistical Topology emerged since topological aspects continue to gain importance in many areas of physics. It is most desirable to study topological invariants and their statistics in schematic models that facilitate the identification of…
Inner functions are an important and popular object of study in the field of complex function theory. We look at meromorphic inner functions with a given spectrum and provide sufficient conditions for them to have uniformly bounded…
In the present paper, we study a new kind of anabelian phenomenon concerning the smooth pointed stable curves in positive characteristic. It shows that the topological structures of moduli spaces of curves can be understood from the…