Premium
Topology on the Spaces Of Orderings of Groups
Author(s) -
Sikora Adama S.
Publication year - 2004
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609303003060
Subject(s) - mathematics , abelian group , mathematics subject classification , cantor set , topology (electrical circuits) , space (punctuation) , topological group , topological space , pure mathematics , set (abstract data type) , group (periodic table) , discrete mathematics , combinatorics , philosophy , linguistics , chemistry , organic chemistry , computer science , programming language
A natural topology on the space of left orderings of an arbitrary semi‐group is introduced here. This space is proved to be compact, and for free abelian groups it is shown to be homeomorphic to the Cantor set. An application of this result is a new proof of the existence of universal Gröbner bases. 2000 Mathematics Subject Classification 06F15, 13P10 (primary), 06F05, 20F60 (secondary).