On free paratopological groups

N.M. Pyrch; O.V. Ravsky

We consider topological properties of free paratopological groups. We also investigate the relations between separation properties of the free paratopological groups and their bases. Some results on cardinal invariants of free paratopological groups are obtained.

1. Arhangel'skii A.V. Mappings related to topological groups, Dokl. Akad. Nauk SSSR 181(1968), 6, 1303--1306.

2. Banakh T.O., Guran I.Y., Gutik O.V. Free topological inverse semigroups, Matematychni Studii, 17 (2002), 93-101.

3. Engelking R. General topology, Moscow, 1986.

4. Graev M.I. Free topological groups, Izvestiya Akad. Nauk SSSR Ser.Mat.,12 (1948), 279--381.

5. Guran I.Y. Suitable sets for paratopological groups , Abstracts of 4th International Algebraic Conference in Ukraine (Lviv, 2003), 87--88.

6. Guran I.Y., Zarichnyi M.M. Elements of the theory of topological groups, Kiyv 1991.

7. Fay T.H., Ordman E.T., SmithThomas B.V. The free topological groups over rationals. General Topology and its Applications 10(1979), 33--47.

8. Junusov A.S. On quasicomponent of free topological groups, Mat. Issledovania. 74, Kishinev 1983, 163--165.

9. Morris S.A. Maximally almost periodic groups and varieties of topological groups Fundamentae Mahematicae, 84, 1974, $\#$1, 1--4.

10. Pyrch N.M., Ravsky O.V. Free paratopological groups: separation properties, International conference ``Geometric Topology: Infinite-Dimensional Topology, Absolute Extensors, Applications'', Lviv, May 26-30, 2004, 60--61.

11. Ravsky O.V., Paratopological groups I. Matematychni Studii, 16 (2001), 37--48.

12. Ravsky O.V., Paratopological groups II. Matematychni Studii, 17 (2002), 93--101.

13. Romaguera S., Sanchis M., Tkachenko M., Free paratopological groups, Topology Proceedings, 27 (2002), 1--28.

14. Sipacheva O.V., Uspenkii V.V. Free topological groups with no small subgroups and graevs metrics, Bull. Mosc. Univ., Mat.Mech. 1987, $\#$4, 21--24.

15. Tkachuk V.V. Duality with respect to $C_{p}$ functor and cardinal invariants of Sousline type, Mat. zametki 1985, 37, 3, 441--451.

	On free paratopological groups
Author	N.M. Pyrch, O.V. Ravsky Lviv Ivan Franko National University
Abstract	We consider topological properties of free paratopological groups. We also investigate the relations between separation properties of the free paratopological groups and their bases. Some results on cardinal invariants of free paratopological groups are obtained.
Keywords	free topological group, separation property, cardinal invariant
DOI	doi:10.30970/ms.25.2.115-125
Reference	1. Arhangel'skii A.V. Mappings related to topological groups, Dokl. Akad. Nauk SSSR 181(1968), 6, 1303--1306. 2. Banakh T.O., Guran I.Y., Gutik O.V. Free topological inverse semigroups, Matematychni Studii, 17 (2002), 93-101. 3. Engelking R. General topology, Moscow, 1986. 4. Graev M.I. Free topological groups, Izvestiya Akad. Nauk SSSR Ser.Mat.,12 (1948), 279--381. 5. Guran I.Y. Suitable sets for paratopological groups , Abstracts of 4th International Algebraic Conference in Ukraine (Lviv, 2003), 87--88. 6. Guran I.Y., Zarichnyi M.M. Elements of the theory of topological groups, Kiyv 1991. 7. Fay T.H., Ordman E.T., SmithThomas B.V. The free topological groups over rationals. General Topology and its Applications 10(1979), 33--47. 8. Junusov A.S. On quasicomponent of free topological groups, Mat. Issledovania. 74, Kishinev 1983, 163--165. 9. Morris S.A. Maximally almost periodic groups and varieties of topological groups Fundamentae Mahematicae, 84, 1974, $\#$1, 1--4. 10. Pyrch N.M., Ravsky O.V. Free paratopological groups: separation properties, International conference ``Geometric Topology: Infinite-Dimensional Topology, Absolute Extensors, Applications'', Lviv, May 26-30, 2004, 60--61. 11. Ravsky O.V., Paratopological groups I. Matematychni Studii, 16 (2001), 37--48. 12. Ravsky O.V., Paratopological groups II. Matematychni Studii, 17 (2002), 93--101. 13. Romaguera S., Sanchis M., Tkachenko M., Free paratopological groups, Topology Proceedings, 27 (2002), 1--28. 14. Sipacheva O.V., Uspenkii V.V. Free topological groups with no small subgroups and graevs metrics, Bull. Mosc. Univ., Mat.Mech. 1987, $\#$4, 21--24. 15. Tkachuk V.V. Duality with respect to $C_{p}$ functor and cardinal invariants of Sousline type, Mat. zametki 1985, 37, 3, 441--451.
Pages	115-125
Volume	25
Issue	2
Year	2006
Journal	Matematychni Studii
Full text of paper	pdf
Table of content of issue	html