TY - JOUR
AU - Richmond, Bettina
PY - 2008/10/01
Y2 - 2023/10/02
TI - Semigroups and their topologies arising from Green's left quasiorder
JF - Applied General Topology
JA - Appl. Gen. Topol.
VL - 9
IS - 2
SE -
DO - 10.4995/agt.2008.1795
UR - https://ojs.upv.es/index.php/AGT/article/view/1795
SP - 143-168
AB - <p>Given a semigroup (S, ·), Green’s left quasiorder on S is given by a ≤ b if a = u · b for some u ϵ S<sup>1</sup>. We determine which topological spaces with five or fewer elements arise as the specialization topology from Green’s left quasiorder for an appropriate semigroup structure on the set. In the process, we exhibit semigroup structures that yield general classes of finite topological spaces, as well as general classes of topological spaces which cannot be derived from semigroup structures via Green’s left quasiorder.</p>
ER -