ON SEQUENTIAL TOPOLOGICAL GROUPS
0
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
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.
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 (23)
- A.V. Arhangel'skii, "Some types of factor mappings and the relations between classes of topological spaces", Soviet Math. Dokl, 4, pp.1726~1729 (1963)
- A.V. Arhangel'skii, "At-lantis Studies in Mathematics, vol. I", pp.2008, Atlantis Press
- J.R. Boone, "Sequentially quotient mappings", Czechoslovak Math. J, 26(2), pp.174~182 (1976)
- A. Camara, "Interaction of topology and algebra in arithmetic geometry", Ph.D., pp.2013
- R.M. Dudley, "On sequential convergence", Proc. Amer. Math. Soc, 112, pp.483~507 (1964)
- R. Engelking, "General topology" (1977), PWN
- S.P. Franklin, "Spaces in which sequences suffice", Fund. Math, 57, pp.107~115 (1965)
- S.P. Franklin, "Spaces in which sequences suffice II", Fund. Math, 61, pp.51~56 (1967)
- M. Husek, "Sequentially continuous homomorphisms on products of topological groups", Topol. Appl, 70, pp.155~165 (1996)
- K.D. Joshi, "Introduction to General Topology" (1983), New Age International (P) Limited
- J.L. Kelley, "Convergence in topology", Duke Math. J, 17, pp.277~283 (1950)
- V.I. Malykhin, "Subspaces of sequential spaces", Math. Notes, 64(3), pp.351~356 (1998)
- S. Mazur, "On continuous mappings on cartesian products", Fund. Math, 39, pp.229~238 (1952)
- S.A. Morris, "Sequential conditions and freeproducts of topological groups", Proc. Amer. Math. Soc, 103(2), pp.633~638 (1998)
- N. Noble, "The continuity of functions on cartesian products", Trans. Amer. Math. Soc, 149, pp.187~198 (1970)
- J. Nyikos, "Metrizability and Frechet-Urysohn property in topological groups", Proc. Amer. Math. Soc, 83, pp.793~801 (1981)
- L.S. Pontryagin, "Topological groups" (1966), Gordon and Breach Science Publishers Inc.
- A. Shibakov, "Sequential group topology on rationals with intermediate sequential order", Proc. Amer. Math. Soc, 124(8), pp.2599~2607 (1996)
- A. Shibakov, "Sequential topological groups of any sequential order under CH", Fund. Math, 155(1), pp.79~89 (1998)
- A. Shibakov, "Metrizability of sequential topological groups with point-countable k-networks", Proc. Amer. Math. Soc, 126(3), pp.943~947 (1998)
- M. Venkataraman, "Directed sets in topology", Math. Student, 30, pp.99~100 (1962)
- A. Wilansky, "Topology for analysis" (1983), R. E. Krieger Pub. Company Inc.
- C. Xavier, "Sequentially closed sets", (Spanish) Rev. Colombiana Mat, 14(2), pp.111~130 (1980)
