A Galois connection between distance functions and inequality relations

Árpád Száz

Mathematica Bohemica (2002)

  • Volume: 127, Issue: 3, page 437-448
  • ISSN: 0862-7959

Abstract

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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 × ℝ . Moreover, we also investigate a relationship between the functions of S and X S .

How to cite

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Száz, Árpád. "A Galois connection between distance functions and inequality relations." Mathematica Bohemica 127.3 (2002): 437-448. <http://eudml.org/doc/249063>.

@article{Száz2002,
abstract = {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 $X_\{S\}$.},
author = {Száz, Árpád},
journal = {Mathematica Bohemica},
keywords = {distance functions and inequality relations; closure operators and Galois connections; Lipschitz and monotone functions; fixed points; distance functions and inequality relations; closure operators and Galois connections; Lipschitz and monotone functions; fixed points},
language = {eng},
number = {3},
pages = {437-448},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A Galois connection between distance functions and inequality relations},
url = {http://eudml.org/doc/249063},
volume = {127},
year = {2002},
}

TY - JOUR
AU - Száz, Árpád
TI - A Galois connection between distance functions and inequality relations
JO - Mathematica Bohemica
PY - 2002
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 127
IS - 3
SP - 437
EP - 448
AB - 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 $X_{S}$.
LA - eng
KW - distance functions and inequality relations; closure operators and Galois connections; Lipschitz and monotone functions; fixed points; distance functions and inequality relations; closure operators and Galois connections; Lipschitz and monotone functions; fixed points
UR - http://eudml.org/doc/249063
ER -

References

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  1. Lattice Theory, Amer. Math. Soc. Colloq. Publ. 25, Providence, Rhode Island, 1967. (1967) Zbl0153.02501MR0598630
  2. 10.1016/0022-247X(74)90025-0, J. Math. Anal. Appl. 47 (1974), 324–353. (1974) Zbl0286.49015MR0346619DOI10.1016/0022-247X(74)90025-0
  3. 10.1090/S0002-9947-1944-0010556-9, Trans. Amer. Math. Soc. 55 (1944), 514–525. (1944) Zbl0060.06205MR0010556DOI10.1090/S0002-9947-1944-0010556-9
  4. Quasi-Uniform Spaces, Marcel Dekker, New York, 1982. (1982) MR0660063
  5. Fixed point theorems in metric and uniform spaces via the Knaster-Tarski principle, Nonlinear Anal. 32 (1998), 225–233. (1998) MR1491625
  6. 10.2307/2313852, Amer. Math. Monthly 72 (1965), 628–631. (1965) Zbl0128.41002MR0179760DOI10.2307/2313852
  7. 10.1090/S0002-9947-1944-0010555-7, Trans. Amer. Math. Soc. 55 (1944), 493–513. (1944) Zbl0060.06204MR0010555DOI10.1090/S0002-9947-1944-0010555-7
  8. On the extensions, refinements and modifications of relators, (to appear). (to appear) Zbl1042.08001MR1882531
  9. Lattices, Proc. London Math. Soc. 52 (1951), 386–400. (1951) Zbl0044.37901MR0690634
  10. Introduction to Lattice Theory, Academic Press, New York, 1963. (1963) MR0166118

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