Sequentially compact Hausdorff cancellative semigroup is a topological group

Author
B. Bokalo, I. Guran
Lviv University, Department of Mechanics and Mathematics
Abstract
We prove the statement announced in the title
Keywords
sequentially compact, Hausdorff, cancellative semigroup, topological group
DOI
doi:10.30970/ms.6.1.39-40
Reference
1. N. Bourbaki. Elements de mathématique III, Premiere partie. Les structures fundamentales de l'analyse, Livre III, Topologie generale, Chap. II, Groupes topologiques (Theorie elementaire). – Actualistes Sci. et Ind, Hermann, 3me ed., 1961.

2. D. Grant. Sequentially compact cancellative topological semigroups: some progress on the Wallace problem // in “Papers on General Topology and Applications, Seventh Summer Conference at the University of Wisconsin” (Madison, 1991), Annals of the New York Acad. Sci. 1993. vol.704. P.150–154.

3. R. Engelking. General Topology. – PWN, Warszawa, 2nd ed., 1986.

4. H. Pfister. Continuity of the inverse // Proc. Amer. Math. Soc. 1985. 95. P.312–314.

5. E.A. Reznichenko. Extension of functions defined on products of pseudocompact spaces and continuity of the inverse in pseudocompact groups // Topol. and Applic. 1994. 59. P.233–244.

6. D. Robbie, S. Svetlichnyi. An answer to A.D. Wallace's question about countably compact cancellative semigroups // Proc. Amer. Math. Soc. 1996. 124. ¹1. P.325–330.

7. A.A. Yur'eva. Countably compact sequential topological semigroup with two-side cancellations is a topological group // Mat. Studii. 1993. 2. P.23–24 (in Russian). Department of Mathematics, Lviv State University, Lviv, 290602, Ukraine

Pages
39-40
Volume
6
Issue
1
Year
1996
Journal
Matematychni Studii
Full text of paper
pdf
Table of content of issue