Approximation relations on the posets of pseudometrics and of pseudoultrametrics
We show that non-trivial "way below" and "way above" relations on the posets of all pseudometrics and of all pseudoultrametrics on a fixed set $X$ are possible if and only if the set $X$ is finite.
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Vasyl Stefanyk Precarpathian National University
2016-06-01
|
| Series: | Karpatsʹkì Matematičnì Publìkacìï |
| Subjects: | |
| Online Access: | https://journals.pnu.edu.ua/index.php/cmp/article/view/1420 |
| _version_ | 1819051877517492224 |
|---|---|
| author | S.I. Nykorovych |
| author_facet | S.I. Nykorovych |
| author_sort | S.I. Nykorovych |
| collection | DOAJ |
| description | We show that non-trivial "way below" and "way above" relations on the posets of all pseudometrics and of all pseudoultrametrics on a fixed set $X$ are possible if and only if the set $X$ is finite. |
| first_indexed | 2024-12-21T12:10:55Z |
| format | Article |
| id | doaj.art-444eb296edae4b1c867cff3c0582107d |
| institution | Directory Open Access Journal |
| issn | 2075-9827 2313-0210 |
| language | English |
| last_indexed | 2024-12-21T12:10:55Z |
| publishDate | 2016-06-01 |
| publisher | Vasyl Stefanyk Precarpathian National University |
| record_format | Article |
| series | Karpatsʹkì Matematičnì Publìkacìï |
| spelling | doaj.art-444eb296edae4b1c867cff3c0582107d2022-12-21T19:04:34ZengVasyl Stefanyk Precarpathian National UniversityKarpatsʹkì Matematičnì Publìkacìï2075-98272313-02102016-06-018115015710.15330/cmp.8.1.150-1571420Approximation relations on the posets of pseudometrics and of pseudoultrametricsS.I. Nykorovych0Vasyl Stefanyk Precarpathian National University, 57 Shevchenka str., 76018, Ivano-Frankivsk, UkraineWe show that non-trivial "way below" and "way above" relations on the posets of all pseudometrics and of all pseudoultrametrics on a fixed set $X$ are possible if and only if the set $X$ is finite.https://journals.pnu.edu.ua/index.php/cmp/article/view/1420pseudometricpseudoultrametricway belowway above |
| spellingShingle | S.I. Nykorovych Approximation relations on the posets of pseudometrics and of pseudoultrametrics Karpatsʹkì Matematičnì Publìkacìï pseudometric pseudoultrametric way below way above |
| title | Approximation relations on the posets of pseudometrics and of pseudoultrametrics |
| title_full | Approximation relations on the posets of pseudometrics and of pseudoultrametrics |
| title_fullStr | Approximation relations on the posets of pseudometrics and of pseudoultrametrics |
| title_full_unstemmed | Approximation relations on the posets of pseudometrics and of pseudoultrametrics |
| title_short | Approximation relations on the posets of pseudometrics and of pseudoultrametrics |
| title_sort | approximation relations on the posets of pseudometrics and of pseudoultrametrics |
| topic | pseudometric pseudoultrametric way below way above |
| url | https://journals.pnu.edu.ua/index.php/cmp/article/view/1420 |
| work_keys_str_mv | AT sinykorovych approximationrelationsontheposetsofpseudometricsandofpseudoultrametrics |