| Title:
|
A Galois connection between distance functions and inequality relations (English) |
| Author:
|
Száz, Árpád |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
127 |
| Issue:
|
3 |
| Year:
|
2002 |
| Pages:
|
437-448 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Following the ideas of R. DeMarr, we establish a Galois connection between distance functions on a set $S$ and inequality relations on $X_{S}=S \times \mathbb{R}$. Moreover, we also investigate a relationship between the functions of $S$ and $X_{S}$. (English) |
| Keyword:
|
distance functions and inequality relations |
| Keyword:
|
closure operators and Galois connections |
| Keyword:
|
Lipschitz and monotone functions |
| Keyword:
|
fixed points |
| MSC:
|
06A06 |
| MSC:
|
06A15 |
| MSC:
|
47H10 |
| MSC:
|
54E25 |
| MSC:
|
54H25 |
| idZBL:
|
Zbl 1003.54012 |
| idMR:
|
MR1931327 |
| DOI:
|
10.21136/MB.2002.134073 |
| . |
| Date available:
|
2009-09-24T22:03:20Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134073 |
| . |
| Reference:
|
[1] Birkhoff, G.: Lattice Theory.Amer. Math. Soc. Colloq. Publ. 25, Providence, Rhode Island, 1967. Zbl 0153.02501, MR 0598630 |
| Reference:
|
[2] Ekeland, I.: On the variational principle.J. Math. Anal. Appl. 47 (1974), 324–353. Zbl 0286.49015, MR 0346619, 10.1016/0022-247X(74)90025-0 |
| Reference:
|
[3] Everett, C. J.: Closure operators and Galois theory in lattices.Trans. Amer. Math. Soc. 55 (1944), 514–525. Zbl 0060.06205, MR 0010556, 10.1090/S0002-9947-1944-0010556-9 |
| Reference:
|
[4] Fletcher, P., Lindgren, W. F.: Quasi-Uniform Spaces.Marcel Dekker, New York, 1982. MR 0660063 |
| Reference:
|
[5] Jachymski, J. R.: Fixed point theorems in metric and uniform spaces via the Knaster-Tarski principle.Nonlinear Anal. 32 (1998), 225–233. MR 1491625 |
| Reference:
|
[6] DeMarr, R.: Partially ordered spaces and metric spaces.Amer. Math. Monthly 72 (1965), 628–631. Zbl 0128.41002, MR 0179760, 10.2307/2313852 |
| Reference:
|
[7] Ore, O.: Galois connexions.Trans. Amer. Math. Soc. 55 (1944), 493–513. Zbl 0060.06204, MR 0010555, 10.1090/S0002-9947-1944-0010555-7 |
| Reference:
|
[8] Pataki, G.: On the extensions, refinements and modifications of relators.(to appear). Zbl 1042.08001, MR 1882531 |
| Reference:
|
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| Reference:
|
[10] Szász, G.: Introduction to Lattice Theory.Academic Press, New York, 1963. MR 0166118 |
| . |
