A NONHOMOGENEOUS ZERO-DIMENSIONAL X SUCH THAT X-X-X IS A GROUP

Authors
VANENGELEN F
Citation
F. Vanengelen, A NONHOMOGENEOUS ZERO-DIMENSIONAL X SUCH THAT X-X-X IS A GROUP, Proceedings of the American Mathematical Society, 124(8), 1996, pp. 2589-2598
Citations number
17
Categorie Soggetti
Mathematics, General",Mathematics,Mathematics
Journal title
Proceedings of the American Mathematical Society → ACNP
ISSN journal
00029939
Volume
124
Issue
8
Year of publication
1996
Pages
2589 - 2598
Database
ISI
SICI code
0002-9939(1996)124:8<2589:ANZXST>2.0.ZU;2-E
Abstract
We provide an example of a zero-dimensional (separable metric) absolut e Borel set X which is not homogeneous, but whose square X x X admits the structure of a topological group. We also construct a zero-dimensi onal absolute Borel set Y such that Y is a homogeneous non-group but Y x Y is a group. This answers questions of Arhangel'skii and Zhou.