Some separation axioms in topological inverse semigroups
by
Péter Körtesi
University of Miskolc, Hungary

In topological groups the separation axioms T₀ and T₂ are equivalent. This equivalence disappears if we consider more general algebric structures like inverse semigroups or weaken the connection between the topological and algebraic structures.

A. Conte gave sufficient conditions for topological inverse semigroups which ensure the validity of separation axioms T₀, T₁, T₂ and those falling between T₀ and T₁ ([1], [2]).

The aim of this presentation is to study the separation axioms between T₁ and T₂, the axiom T₃, and also some order separation axioms introduced by McCartan [3] in semitopological groups and semitopological and topological inverse semigroups.

The given conditions show the importance of the set of idempotents for the separation of inverse semigroups.

References

1. A.Conte : Assiomi di separazione nei gruppidi topologici, Richerche di Matematica 17 (1969), 168-180.
2. A.Conte : Gruppidi topologici soddisfacenti ad assiomi de separationi intermedi fra T₀ e T₁, Atti. Accad. Sci. Torino Cl. Sci. Fis. Mat. Nat. 105 (1971), 185-193.
3. McCartan : Separation axioms for topological ordered spaces, Proc. Camb. Phil. Soc. 64 (1968), 965-973.

Date received: July 1, 1997

Copyright © 1997 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caao-72.