Related papers: Topos Methods in the Foundations of Physics
This is a detailed introductory survey of the cohomological dimension theory of compact metric spaces.
The purpose of this thesis is to study classical combinatorial objects, such as polytopes, polytopal complexes, and subspace arrangements, using tools that have been developed in combinatorial topology, especially those tools developed in…
We explore possibilities and limitations of a purely topological approach to the Dvoretzky Theorem.
This is an attempt to look at the tropical geometry from topological point of view.
A very brief introduction to tropical and idempotent mathematics is presented. Applications to classical mechanics and geometry are especially examined.
This document is an introduction to and review of two-dimensional mathematical physics. The reader is introduced to the subject matter primarily through problems, which are presented along with detailed worked solutions. For each chapter,…
The construction of an ontology of scientific knowledge objects, presented here, is part of the development of an approach oriented towards the visualization of scientific knowledge. It is motivated by the fact that the concepts that are…
This Resource Letter provides a guide to the literature on the geometric angles and phases in classical and quantum physics. Journal articles and books are cited for the following topics: anticipations of the geometric phase, foundational…
We present a general approach for the formulation of equations of motion for compact objects in general relativistic theories. The particle is assumed to be moving in a geometric background which in turn is asymptotically flat. Our approach…
The article is an historical overview of some of the major contributions from different areas of Science with which, for centuries, it has been built up a scientific, sound and consistent vision of the atom. Some experiments that led us to…
An expository hitchhikers guide to some theorems in mathematics.
We present mathematical details of several cosmological models, whereby the topological and the geometrical background will be emphasized.
Ideas from quantum field theory and topology have proved remarkably fertile in suggesting new phenomena in the quantum physics of condensed matter. Here I'll supply some broad, unifying context, both conceptual and historical, for the…
In this text we expose basic cases of some fundamental ideas and methods of topology. Namely, of homotopy, degree, fundamental group, covering, Whitehead invariant, etc. This is done by considering the elementary example: closed polygonal…
We present a way of topologizing sets of Galois types over structures in abstract elementary classes with amalgamation. In the elementary case, the topologies thus produced refine the syntactic topologies familiar from first order logic. We…
Using ideas from synthetic topology, a new approach to descriptive set theory is suggested. Synthetic descriptive set theory promises elegant explanations for various phenomena in both classic and effective descriptive set theory.…
This purpose of this book is twofold: to provide a general introduction to higher category theory (using the formalism of "quasicategories" or "weak Kan complexes"), and to apply this theory to the study of higher versions of Grothendieck…
We discuss a formal system of mathematics. We use it to construct the natural numbers.
We look for a deep connection between mathematics and physics. Our approach is to propose a set theory T which leads to a concise mathematical description of physical fields and to a finite unit of action. The concept of "definability" of…
An introduction to modern theories for the origin of structure in the Universe is given. After a brief review of the growth of cosmological perturbations in an expanding Universe and a summary of some important observational results, the…