Topological semigroups of matrix units

• Published in: Algebra and Discrete Mathematics
• Date: 2005
• Main Authors: Gutik, O.V., Pavlyk, K.P.
• Format: Article
• Language: English
• Published: Інститут прикладної математики і механіки НАН України 2005
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/157194
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Topological semigroups of matrix units / O.V. Gutik, K.P. Pavlyk // Algebra and Discrete Mathematics. — 2005. — Vol. 4, № 3. — С. 1–17. — Бібліогр.: 26 назв. — англ.

We prove that the semigroup of matrix units is
 stable. Compact, countably compact and pseudocompact topologies τ on the infinite semigroup of matrix units Bλ such that (Bλ,τ )
 is a semitopological (inverse) semigroup are described. We prove
 the following properties of an infinite topological semigroup of matrix units. On the infinite semigroup of matrix units there exists
 no semigroup pseudocompact topology. Any continuous homomorphism from the infinite topological semigroup of matrix units into
 a compact topological semigroup is annihilating. The semigroup
 of matrix units is algebraically h-closed in the class of topological
 inverse semigroups. Some H-closed minimal semigroup topologies
 on the infinite semigroup of matrix units are considered.