ON SEQUENTIAL TOPOLOGICAL GROUPS

다국어 초록 (Multilingual Abstract)

In this paper, we study the sequentially open and closed subsets of sequential topological groups determined by sequentially continuous group homo-morphism. In particular, we investigate the sequentially openness (closedness) and sequentially compactness of subsets of sequential topological groups by the aid of sequentially continuity, sequentially interior or closure operators. Moreover, we explore subgroup and sequential quotient group of a sequential topological group.

참고문헌 (Reference)

1 A. Wilansky, "Topology for analysis" R. E. Krieger Pub. Company Inc. 1983

2 L.S. Pontryagin, "Topological groups" Gordon and Breach Science Publishers Inc. 1966

3 N. Noble, "The continuity of functions on cartesian products" 149 : 187-198, 1970

4 V.I. Malykhin, "Subspaces of sequential spaces" 64 (64): 351-356, 1998

5 S.P. Franklin, "Spaces in which sequences suffice II" 61 : 51-56, 1967

6 S.P. Franklin, "Spaces in which sequences suffice" 57 : 107-115, 1965

7 A.V. Arhangel'skii, "Some types of factor mappings and the relations between classes of topological spaces" 4 : 1726-1729, 1963

8 J.R. Boone, "Sequentially quotient mappings" 26 (26): 174-182, 1976

9 M. Husek, "Sequentially continuous homomorphisms on products of topological groups" 70 : 155-165, 1996

10 C. Xavier, "Sequentially closed sets" 14 (14): 111-130, 1980

11 A. Shibakov, "Sequential topological groups of any sequential order under CH" 155 (155): 79-89, 1998

12 A. Shibakov, "Sequential group topology on rationals with intermediate sequential order" 124 (124): 2599-2607, 1996

13 S.A. Morris, "Sequential conditions and freeproducts of topological groups" 103 (103): 633-638, 1998

14 R.M. Dudley, "On sequential convergence" 112 : 483-507, 1964

15 S. Mazur, "On continuous mappings on cartesian products" 39 : 229-238, 1952

16 A. Shibakov, "Metrizability of sequential topological groups with point-countable k-networks" 126 (126): 943-947, 1998

17 J. Nyikos, "Metrizability and Frechet-Urysohn property in topological groups" 83 : 793-801, 1981

18 K.D. Joshi, "Introduction to General Topology" New Age International (P) Limited 1983

19 A. Camara, "Interaction of topology and algebra in arithmetic geometry" The University of Nottingham 2013

20 R. Engelking, "General topology" PWN 1977

21 M. Venkataraman, "Directed sets in topology" 30 : 99-100, 1962

22 J.L. Kelley, "Convergence in topology" 17 : 277-283, 1950

23 A.V. Arhangel'skii, "At-lantis Studies in Mathematics, vol. I" Atlantis Press/World Scientic 2008