Algebraic approach to locally finite trees with one end

Zelinka, Bohdan. "Algebraic approach to locally finite trees with one end." Mathematica Bohemica 128.1 (2003): 37-44. <http://eudml.org/doc/249228>.

@article{Zelinka2003,
abstract = {Let $T$ be an infinite locally finite tree. We say that $T$ has exactly one end, if in $T$ any two one-way infinite paths have a common rest (infinite subpath). The paper describes the structure of such trees and tries to formalize it by algebraic means, namely by means of acyclic monounary algebras or tree semilattices. In these algebraic structures the homomorpisms and direct products are considered and investigated with the aim of showing, whether they give algebras with the required properties. At the end some further assertions on the structure of such trees are stated, without the algebraic formalization.},
author = {Zelinka, Bohdan},
journal = {Mathematica Bohemica},
keywords = {locally finite tree; one-way infinite path; acyclic monounary algebra; tree semilattice; locally finite tree; one-way infinite path; acyclic monounary algebra; tree semilattice},
language = {eng},
number = {1},
pages = {37-44},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Algebraic approach to locally finite trees with one end},
url = {http://eudml.org/doc/249228},
volume = {128},
year = {2003},
}

TY - JOUR
AU - Zelinka, Bohdan
TI - Algebraic approach to locally finite trees with one end
JO - Mathematica Bohemica
PY - 2003
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 128
IS - 1
SP - 37
EP - 44
AB - Let $T$ be an infinite locally finite tree. We say that $T$ has exactly one end, if in $T$ any two one-way infinite paths have a common rest (infinite subpath). The paper describes the structure of such trees and tries to formalize it by algebraic means, namely by means of acyclic monounary algebras or tree semilattices. In these algebraic structures the homomorpisms and direct products are considered and investigated with the aim of showing, whether they give algebras with the required properties. At the end some further assertions on the structure of such trees are stated, without the algebraic formalization.
LA - eng
KW - locally finite tree; one-way infinite path; acyclic monounary algebra; tree semilattice; locally finite tree; one-way infinite path; acyclic monounary algebra; tree semilattice
UR - http://eudml.org/doc/249228
ER -