Categorical Nonstandard Analysis
نویسندگان
چکیده
In the present paper, we propose a new axiomatic approach to nonstandard analysis and its application general theory of spatial structures in terms category theory. Our framework is based on idea internal set theory, while make use an endofunctor U topos sets S together with natural transformation υ, instead as “standard”, “internal”, or “external”. Moreover, notion space called U-space, USpace whose objects are U-spaces morphisms functions U-spatial morphisms. The USpace, which shown be Cartesian closed, gives unified viewpoint toward topological coarse geometric structure. It will also useful further study symmetries/asymmetries systems infinite degrees freedom, such quantum fields.
منابع مشابه
Nonstandard Functional Interpretations and Categorical Models
Recently, the second author, Briseid and Safarik introduced nonstandard Dialectica, a functional interpretation that is capable of eliminating instances of familiar principles of nonstandard arithmetic including overspill, underspill, and generalisations to higher types from proofs. We show that, under few metatheoretical assumptions, the properties of this interpretation are mirrored by first ...
متن کاملNonstandard Analysis in Point
We present Nonstandard Analysis by three axioms: the Extension, Transfer and Saturation Principles in the framework of the superstructure of a given innnite set. We also present several applications of this axiomatic approach to point-set topology. Some of the topological topics such as the Hewitt realcompactiication and the nonstandard characterization of the sober spaces seem to be new in the...
متن کاملNonstandard Analysis of Graphs
Intuitively, it is tempting to view a cube in R as a discrete lattice with infinitesimal edges. A similar infinitesimal picture suggests itself with other fractal spaces such as the Sierpinski gasket or the Sierpinski sponge (see [13], [5].) The purpose of this paper is to show certain classes of metric spaces characterized by volume growth properties of balls ([4],[2]) can viewed as graphs wit...
متن کاملNon-nonstandard Analysis
There is an ancient philosphical-religious divide over questions of infinity. This divide extends over mathematics and we see it in many forms. A perfect example is offered by the twin approaches to analysis: limits and infinitesimals. With Robinson’s discovery of nonstandard analysis, both approaches have achieved legitimacy. Today, there is a new approach, non-nonstandard analysis, which, in ...
متن کاملA New Approach to Nonstandard Analysis
In this paper, we propose a new approach to nonstandard analysis without using the ultrafilters. This method is very simple in practice. Moreover, we construct explicitly the total order relation in the new field of the infinitesimal numbers. To illustrate the importance of this work, we suggest comparing a few applications of this approach with the former methods.
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: Symmetry
سال: 2021
ISSN: ['0865-4824', '2226-1877']
DOI: https://doi.org/10.3390/sym13091573