International Journal of Mathematics and Mathematical Sciences
Volume 2010 (2010), Article ID 671401, 13 pages
doi:10.1155/2010/671401
Research Article

Brandt Extensions and Primitive Topological Inverse Semigroups

Tetyana Berezovski,1 Oleg Gutik,2 and Kateryna Pavlyk2,3

1Department of Math/CSC, Saint Joseph's University, 5600 City Avenue, Philadelphia, PA 19131, USA
2Department of Mathematics, Ivan Franko Lviv National University, Universytetska 1, Lviv 79000, Ukraine
3Pidstrygach Institute for Applied Problems of Mechanics and Mathematics, National Academy of Sciences, Naukova 3b, Lviv 79060, Ukraine

Received 20 July 2009; Accepted 1 February 2010

Academic Editor: Volker Runde

Copyright © 2010 Tetyana Berezovski et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study (countably) compact and (absolutely) H-closed primitive topological inverse semigroups. We describe the structure of compact and countably compact primitive topological inverse semigroups and show that any countably compact primitive topological inverse semigroup embeds into a compact primitive topological inverse semigroup.