Related papers: Priestley perspective on pointfree topology
We use double categories to obtain a single theorem characterizing certain exponentiable morphisms of small categories, topological spaces, locales, and posets.
In this paper we study the class of modules with fusion and implication based over distributive lattices, or FIDL-modules, for short. We introduce the concepts of FIDL-subalgebra and FIDL-congruence as well as the notions of simple and…
We describe topological T-duality and Poisson-Lie T-duality in terms of QP (differential graded symplectic) manifolds and their canonical transformations. Duality is mediated by a QP-manifold on doubled non-abelian "correspondence" space,…
This review aims to cover the central aspects of current research in cosmic topology from a topological and observational perspective. Beginning with an overview of the basic concepts of cosmology, it is observed that though a determinant…
The paper studies computability-theoretic aspects of topological $T_0$-spaces. We introduce effective versions of the notions of a countable $c$-poset and a (second-countable) topological space with base. Based on this, we prove an…
We formulate symmetric versions of classical variational principles. Within the framework of non-smooth critical point theory, we detect Palais-Smale sequences with additional second order and symmetry information. We discuss applications…
We provide a pointwise bipolar theorem for liminf-closed convex sets of positive Borel measurable functions on a sigma-compact metric space without the assumption that the polar is a tight set of measures. As applications we derive a…
We introduce the notion of a topological geodesic in a 3-manifold. Under suitable hypotheses on the fundamental group, for instance word-hyperbolicity, topological geodesics are shown to have the useful properties of, and play the same role…
A tutorial introduction to projective geometric algebra (PGA), a modern, coordinate-free framework for doing euclidean geometry. PGA features: uniform representation of points, lines, and planes; robust, parallel-safe join and meet…
The aim of this article is to review different generalizations of the the notion of topological complexity to the equivariant setting. In particular, we review the relation (or non-relation) between these notions and the topological…
Probabilistic independence can dramatically simplify the task of eliciting, representing, and computing with probabilities in large domains. A key technique in achieving these benefits is the idea of graphical modeling. We survey existing…
The theory of multidimensional persistent homology was initially developed in the discrete setting, and involved the study of simplicial complexes filtered through an ordering of the simplices. Later, stability properties of…
First, we define some concepts similar to the local compactoidity or the c-compactness, and study relationships between these concepts and the original ones. As a result, we find a characterization of the local compactoidity when its…
By generalizing the notion of linearization, a concept originally arising from microlocal analysis and symbolic calculus, to diffeological spaces, we make a first proposal setting for optimization problems in this category. We show how…
Recently the duality map between electric-like asymptotic charges of $p$-form gauge theories is studied. The outcome is an existence and uniqueness theorem and the topological nature of the duality map. The goal of this work is to extend…
For surfaces without boundary, nonlocal notions of directional and mean curvatures have been recently given. Here, we develop alternative notions, special cases of which apply to surfaces with boundary. Our main tool is a new fractional or…
We compute the cohomology of the right generalised projective Stiefel manifolds and use it to find bounds on the rank of the complementary bundle for certain vector bundles. Further the cohomology computations are also used to find bounds…
Ranking or assessing centrality in multivariate and non-Euclidean data is difficult because there is no canonical order and many depth notions become computationally fragile in high-dimensional or structured settings. We introduce a…
Topological Data Analysis (TDA) allows us to extract powerful topological and higher-order information on the global shape of a data set or point cloud. Tools like Persistent Homology or the Euler Transform give a single complex description…
This paper introduces a model that identifies spatial relationships for a structural analysis based on the concept of simplicial complex. The spatial relationships are identified through overlapping two map layers, namely a primary layer…