Open AccessIntroduction to Hyperspaces
Author(s) -
Mark Burgin
Publication year - 2021
Publication title -
international journal of pure mathematics
Language(s) - English
Resource type - Journals
ISSN - 2313-0571
DOI - 10.46300/91019.2020.7.5
Subject(s) - infinity , transfinite number , mathematics , variety (cybernetics) , contrast (vision) , series (stratigraphy) , mathematical structure , pure mathematics , calculus (dental) , algebra over a field , computer science , mathematical analysis , mathematics education , medicine , paleontology , statistics , dentistry , artificial intelligence , biology
The development of mathematics brought mathematicians to infinite structures. This process started with transcendent real numbers and infinite sequences going through infinite series to transfinite numbers to nonstandard numbers to hypernumbers. From mathematics, infinity came to physics where physicists have been trying to get rid of infinity inventing a variety of techniques for doing this. In contrast to this, mathematicians as well as some physicists suggested ways to work with infinity introducing new mathematical structures such distributions and extrafunctions. The goal of this paper is to extend mathematical tools for treating infinity by considering hyperspaces and developing their theory.