A sheaf-theoretic foundation for nonstandard analysis
نویسندگان
چکیده
منابع مشابه
Remarks on a Constructive Sheaf Model of Nonstandard Analysis
The sheaves over the category of lters, with a joint cover topology, serve as a universe of sets where nonstandard analysis can be developed along constructive principles. In this paper we show that all functions between internal sets in this model are internal. We also illustrate how this model can be used by giving a constructive nonstandard proof of the Implicit Function Theorem.
متن کاملSheaf-Theoretic Stratification Learning
In this paper, we investigate a sheaf-theoretic interpretation of stratification learning. Motivated by the work of Alexandroff (1937) and McCord (1978), we aim to redirect efforts in the computational topology of triangulated compact polyhedra to the much more computable realm of sheaves on partially ordered sets. Our main result is the construction of stratification learning algorithms framed...
متن کاملSheaf Theoretic Formulation of Entanglement
A formulation in terms of sheaf theoretic (or categorical) notions for quantum entanglement is given with direct experimental consequences. The notions from sheaf theory and category theory give structural theory, i.e., qualitative theory, as a candidate for quantum gravity. Its advantage is the following: it provides not only space-time background independent, but also scale independent.This t...
متن کاملA Sheaf-theoretic View of Loop Spaces
The context of enriched sheaf theory introduced in the author’s thesis provides a convenient viewpoint for models of the stable homotopy category as well as categories of finite loop spaces. Also, the languages of algebraic geometry and algebraic topology have been interacting quite heavily in recent years, primarily due to the work of Voevodsky and that of Hopkins. Thus, the language of Grothe...
متن کاملA Circuit-theoretic Anomaly Resolved by Nonstandard Analysis
An anomaly in circuit theory is the disappearance of some of the stored energy when two capacitors, one charged and the other uncharged, are connected together through resistanceless wires. Nonstandard analysis shows that, when the wires are taken to have infinitesimally small but nonzero resistance, the energy dissipated in the wires equals that substantial amount of energy that had disappeare...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Annals of Pure and Applied Logic
سال: 1997
ISSN: 0168-0072
DOI: 10.1016/s0168-0072(96)00041-3