Related papers: Synthetic Topology and Constructive Metric Spaces
We discuss topological versions of the closed graph theorem, where continuity is inferred from near continuity in tandem with suitable conditions on source or target spaces. We seek internal characterizations of spaces satisfying a closed…
The idea of slicing divergences has been proven to be successful when comparing two probability measures in various machine learning applications including generative modeling, and consists in computing the expected value of a `base…
How does the topological space of science emerge? Inspired by the concept of maps of science, i.e. mapping scientific topics to a scientific space, we ask which topological structure a dynamical process of authors collaborating and…
In this survey, my aim has been to discuss the use of sequences and countable sets in general topology. In this way I have been led to consider five different classes of topological spaces: first countable spaces, sequential spaces, Frechet…
A fundamental characteristic of computer networks is their topological structure. The question of the description of the structural characteristics of computer networks represents a problem that is not completely solved. Search methods for…
On objects of a triangulated category with a stability condition, we construct a topology.
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…
Deep metric learning aims to learn embeddings that contain semantic similarity information among data points. To learn better embeddings, methods to generate synthetic hard samples have been proposed. Existing methods of synthetic hard…
Borrowing elementary ideas from solid mechanics and differential geometry, this presentation shows that the volume swept by a regular solid undergoing a wide class of volume-preserving deformations induces a rather natural metric structure…
Reversibility is a key issue in the interface between computation and physics, and of growing importance as miniaturization progresses towards its physical limits. Most foundational work on reversible computing to date has focussed on…
The schematic finite spaces are those finite ringed spaces where a theory of quasi-coherent modules can be developed with minimal natural conditions. We give various characterizations of these spaces and their natural morphisms. We show…
The paper presents a topology optimization approach that designs an optimal structure, called a self-supporting structure, which is ready to be fabricated via additive manufacturing without the usage of additional support structures. Such…
The context of this paper is the use of formal methods for topology-based geometric modelling. Topology-based geometric modelling deals with objects of various dimensions and shapes. Usually, objects are defined by a graph-based topological…
This paper explores the concept of topological transitivity in nonautonomous dynamical systems, which are defined as sequences of continuous maps from a compact metric space to itself. It investigates various conditions (including…
We introduce cs-topologies, or topologies of open complemented subsets, as a new approach to constructive topology that preserves the duality between open and closed subsets of classical topology. Complemented subsets were used successfully…
For every finite closure space $X$ one can define a finite topological space $\operatorname{Top} X$ together with a natural projection $\operatorname{Top} X\longrightarrow X$. This could allow to apply the techniques of topological…
This article presents a novel mathematical formalism for advanced manifold--metric pairs, enhancing the frameworks of geometry and topology. We construct various D-dimensional manifolds and their associated metric spaces using functional…
Computational topology is a vibrant contemporary subfield and this article integrates knot theory and mathematical visualization. Previous work on computer graphics developed a sequence of smooth knots that were shown to converge point wise…
Abstract axiomatic formulation of mathematical structures are extensively used to describe our physical world. We take here the reverse way. By making basic assumptions as starting point, we reconstruct some features of both geometry and…
The generation of synthetic data is an essential tool to study complex systems, allowing for example to test models of these in precisely controlled settings, or to parametrize simulation models when data is missing. This paper focuses on…