Class preserving mappings of equivalence systems

Chajda, Ivan. "Class preserving mappings of equivalence systems." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 43.1 (2004): 61-64. <http://eudml.org/doc/32345>.

@article{Chajda2004,
abstract = {By an equivalence system is meant a couple $\mathcal \{A\} = (A,\theta )$ where $A$ is a non-void set and $\theta $ is an equivalence on $A$. A mapping $h$ of an equivalence system $\mathcal \{A\}$ into $\mathcal \{B\}$ is called a class preserving mapping if $h([a]_\{\theta \}) = [h(a)]_\{\theta \{^\{\prime \}\}\}$ for each $a \in A$. We will characterize class preserving mappings by means of permutability of $\theta $ with the equivalence $\Phi _\{h\}$ induced by $h$.},
author = {Chajda, Ivan},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {equivalence relation; equivalence system; relational system; homomorphism; strong homomorphism; permuting equivalences; equivalence relation},
language = {eng},
number = {1},
pages = {61-64},
publisher = {Palacký University Olomouc},
title = {Class preserving mappings of equivalence systems},
url = {http://eudml.org/doc/32345},
volume = {43},
year = {2004},
}

TY - JOUR
AU - Chajda, Ivan
TI - Class preserving mappings of equivalence systems
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2004
PB - Palacký University Olomouc
VL - 43
IS - 1
SP - 61
EP - 64
AB - By an equivalence system is meant a couple $\mathcal {A} = (A,\theta )$ where $A$ is a non-void set and $\theta $ is an equivalence on $A$. A mapping $h$ of an equivalence system $\mathcal {A}$ into $\mathcal {B}$ is called a class preserving mapping if $h([a]_{\theta }) = [h(a)]_{\theta {^{\prime }}}$ for each $a \in A$. We will characterize class preserving mappings by means of permutability of $\theta $ with the equivalence $\Phi _{h}$ induced by $h$.
LA - eng
KW - equivalence relation; equivalence system; relational system; homomorphism; strong homomorphism; permuting equivalences; equivalence relation
UR - http://eudml.org/doc/32345
ER -