| Постоянная ссылка (СИД2) |
J2169917586 |
| Название |
HOPF-TYPE THEOREMS FOR /-NEIGHBORS |
| Автор |
Malyutin A. V. |
| Автор |
Shirokov I. M. |
| Источник |
Сибирские электронные математические известия |
| Страницы/Объём |
165-182 |
| Сокращ. назв. источника |
Сиб. электрон. мат. изв. |
| Год |
2023 |
| Том |
20 |
| Номер |
1 |
| Адрес в Интернет |
http://elibrary.ru/item.asp?id=54768287 |
| Постоянная ссылка (СИД) |
J21699175 |
| Ключевые слова (авторские) |
Borsuk-Ulam type theorems%locally injective%the Hopf theorem%winding number |
| Место хранения |
Удаленный доступ. Эл. регистр. НЭБ |
| Дата регистрации в ВИНИТИ |
06.11.2023 |
| Язык текста |
английский |
| Аннотация |
We work within the framework of a program aimed at exploring various extended versions for theorems from a class containing Borsuk-Ulam type theorems, some fixed point theorems, the KKM lemma, Radon, Tverberg, and Helly theorems. In this paper we study variations of the Hopf theorem concerning continuous maps of a compact Riemannian manifold M of dimension n tо Rn. First, we generalize the Hopf theorem in a quantitative sense. Then we investigate the case of maps f: M м Rm with n < m and introduce several notions of varied types of f-nciglibors. winch is a pair of distinct points m M such that f takes it to a 'small' set of some type. Next for each type, we ask what distances on M are realized as distances between f-nciglibors of tins type and study various characteristics of this set of distances. One of our main results is as follows. Let f: M м Rm be a continuous map. We say that two distinct points a and b in M are visual f-neighbors if the segment in Rm with on dpoints f (a) at id f (b) inter sects f (M) onR' at f (a) at id f (b). Then the set of distances that are realized as distances between visual f-neiglil>ors is infinite |
| Тематический раздел |
Математика |