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Volumn 221, Issue 2, 2013, Pages 95-127

On a generalization of Abelian sequential groups

Author keywords

Abelian group; Bs group; Com pact Abelian group; Dual group; G closed subgroup; S group; Sequentially covering map; T sequence; TB sequence

Indexed keywords


EID: 84877710261     PISSN: 00162736     EISSN: None     Source Type: Journal    
DOI: 10.4064/fm221-2-1     Document Type: Article
Times cited : (11)

References (53)
  • 3
    • 0242694349 scopus 로고    scopus 로고
    • Contributions to the duality theory of abelian topological groups and to the theory of nuclear groups
    • L. Außenhofer, Contributions to the duality theory of Abelian topological groups and to the theory of nuclear groups, Dissertationes Math. 384 (1999).
    • (1999) Dissertationes Math. , vol.384
    • Außenhofer, L.1
  • 5
    • 84871337442 scopus 로고    scopus 로고
    • On reflexive group topologies on abelian groups of finite exponent
    • L. Außenhofer and S. S. Gabriyelyan, On reflexive group topologies on Abelian groups of finite exponent, Arch. Math. (Basel) 99 (2012), 583-588.
    • (2012) Arch. Math. (Basel) , vol.99 , pp. 583-588
    • Außenhofer, L.1    Gabriyelyan, S.S.2
  • 6
    • 77957907709 scopus 로고    scopus 로고
    • Topologies on groups determined by sequences: Answers to several questions of I. Protasov and e. zelenyuk
    • T. O. Banakh, Topologies on groups determined by sequences: answers to several questions of I. Protasov and E. Zelenyuk, Mat. Stud. 15 (2001), 145- 150.
    • (2001) Mat. Stud. , vol.15 , pp. 145-150
    • Banakh, T.O.1
  • 8
    • 0038307388 scopus 로고    scopus 로고
    • Answer to raczkowski's questions on convergent sequences of integers
    • G. Barbieri, D. Dikranjan, C. Milan and H. Weber, Answer to Raczkowski's questions on convergent sequences of integers, Topology Appl. 132 (2003), 89-101.
    • (2003) Topology Appl. , vol.132 , pp. 89-101
    • Barbieri, G.1    Dikranjan, D.2    Milan, C.3    Weber, H.4
  • 9
    • 55449131355 scopus 로고    scopus 로고
    • Topological torsion related to some recursive sequences of integers
    • G. Barbieri, D. Dikranjan, C. Milan and H. Weber, Topological torsion related to some recursive sequences of integers, Math. Nachr. 281 (2008), 930-950.
    • (2008) Math. Nachr. , vol.281 , pp. 930-950
    • Barbieri, G.1    Dikranjan, D.2    Milan, C.3    Weber, H.4
  • 10
    • 85009953982 scopus 로고    scopus 로고
    • Characterizations of groups generated by kronecker sets
    • A. Bir'o, Characterizations of groups generated by Kronecker sets, J. Th'eor. Nombres Bordeaux 19 (2007), 567-582.
    • (2007) J. th'Eor. Nombres Bordeaux , vol.19 , pp. 567-582
    • Bir'O, A.1
  • 11
    • 84863110723 scopus 로고    scopus 로고
    • Pontryagin duality in the class of precompact abelian groups and the baire property
    • M. Bruguera and M. Tkachenko, Pontryagin duality in the class of precompact Abelian groups and the Baire property, J. Pure Appl. Algebra 216 (2012), 2636-2647.
    • (2012) J. Pure Appl. Algebra , vol.216 , pp. 2636-2647
    • Bruguera, M.1    Tkachenko, M.2
  • 12
    • 0032221011 scopus 로고    scopus 로고
    • Pontryagin duality for metrizable groups
    • M. J. Chasco, Pontryagin duality for metrizable groups, Arch. Math. (Basel) 70 (1998), 22-28.
    • (1998) Arch. Math. (Basel) , vol.70 , pp. 22-28
    • Chasco, M.J.1
  • 13
    • 84860794184 scopus 로고    scopus 로고
    • A survey on reflexivity of abelian topological groups
    • M. J. Chasco, D. Dikranjan and E. Mart'in-Peinador, A survey on reflexivity of abelian topological groups, Topology Appl. 159 (2012), 2290-2309.
    • (2012) Topology Appl. , vol.159 , pp. 2290-2309
    • Chasco, M.J.1    Dikranjan, D.2    Mart'In-Peinador, E.3
  • 14
    • 0042429203 scopus 로고    scopus 로고
    • Topologies on the direct sum of topological abelian groups
    • M. J. Chasco and X. Dom'inguez, Topologies on the direct sum of topological Abelian groups, Topology Appl. 133 (2003), 209-223.
    • (2003) Topology Appl. , vol.133 , pp. 209-223
    • Chasco, M.J.1    Dom'Inguez, X.2
  • 15
    • 78650708898 scopus 로고    scopus 로고
    • Schwartz groups and con- vergence of characters
    • M. J. Chasco, X. Dom'inguez and V. Tarieladze, Schwartz groups and con- vergence of characters, Topology Appl. 158 (2011), 484-491.
    • (2011) Topology Appl. , vol.158 , pp. 484-491
    • Chasco, M.J.1    Dom'Inguez, X.2    Tarieladze, V.3
  • 16
    • 33751524938 scopus 로고    scopus 로고
    • A class of angelic se- quential non-fr'echet-urysohn topological groups
    • M. J. Chasco, E. Mart'in-Peinador and V. Tarieladze, A class of angelic se- quential non-Fr'echet-Urysohn topological groups, Topology Appl. 154 (2007), 741-748.
    • (2007) Topology Appl. , vol.154 , pp. 741-748
    • Chasco, M.J.1    Mart'In-Peinador, E.2    Tarieladze, V.3
  • 17
    • 0030601036 scopus 로고    scopus 로고
    • Relating a locally compact abelian group to its bohr compactification
    • W. W. Comfort, S. Hern'andez and F. J. Trigos-Arrieta, Relating a locally compact Abelian group to its Bohr compactification, Adv. Math. 120 (1996), 322-344.
    • (1996) Adv. Math. , vol.120 , pp. 322-344
    • Comfort, W.W.1    Hern'Andez, S.2    Trigos-Arrieta, F.J.3
  • 18
    • 0000816928 scopus 로고
    • Topologies induced by groups of characters
    • W. W. Comfort and K. A. Ross, Topologies induced by groups of characters, Fund. Math. 55 (1964), 283-291.
    • (1964) Fund. Math. , vol.55 , pp. 283-291
    • Comfort, W.W.1    Ross, K.A.2
  • 19
    • 33750466571 scopus 로고    scopus 로고
    • Characterizing subgroups of compact abelian groups
    • D. Dikranjan and K. Kunen, Characterizing subgroups of compact abelian groups, J. Pure Appl. Algebra 208 (2007), 285-291.
    • (2007) J. Pure Appl. Algebra , vol.208 , pp. 285-291
    • Dikranjan, D.1    Kunen, K.2
  • 20
    • 14744282992 scopus 로고    scopus 로고
    • A characterization of the maximally almost periodic abelian groups
    • D. Dikranjan, C. Milan and A. Tonolo, A characterization of the maximally almost periodic abelian groups, J. Pure Appl. Algebra 197 (2005), 23-41.
    • (2005) J. Pure Appl. Algebra , vol.197 , pp. 23-41
    • Dikranjan, D.1    Milan, C.2    Tonolo, A.3
  • 21
    • 0000216378 scopus 로고
    • Zur Bohr-Konvergenz der Folgen
    • P. Flor, Zur Bohr-Konvergenz der Folgen, Math. Scand. 23 (1968), 169-170.
    • (1968) Math. Scand. , vol.23 , pp. 169-170
    • Flor, P.1
  • 22
    • 0000293411 scopus 로고
    • Spaces in which sequences suffice
    • S. P. Franklin, Spaces in which sequences suffice, Fund. Math. 57 (1965), 107-115.
    • (1965) Fund. Math. , vol.57 , pp. 107-115
    • Franklin, S.P.1
  • 23
    • 77957900171 scopus 로고    scopus 로고
    • Groups of quasi-invariance and the pontryagin duality
    • S. S. Gabriyelyan, Groups of quasi-invariance and the Pontryagin duality, Topology Appl. 157 (2010), 2786-2802.
    • (2010) Topology Appl. , vol.157 , pp. 2786-2802
    • Gabriyelyan, S.S.1
  • 24
    • 77957894946 scopus 로고    scopus 로고
    • On t-sequences and characterized subgroups
    • S. S. Gabriyelyan, On T-sequences and characterized subgroups, Topology Appl. 157 (2010), 2834-2843.
    • (2010) Topology Appl. , vol.157 , pp. 2834-2843
    • Gabriyelyan, S.S.1
  • 25
    • 84860837528 scopus 로고    scopus 로고
    • Characterizable groups: Some results and open questions
    • S. S. Gabriyelyan, Characterizable groups: some results and open questions, Topology Appl. 159 (2012), 2378-2391.
    • (2012) Topology Appl. , vol.159 , pp. 2378-2391
    • Gabriyelyan, S.S.1
  • 26
    • 84871425439 scopus 로고    scopus 로고
    • Topologies on groups determined by sets of convergent sequences
    • S. S. Gabriyelyan, Topologies on groups determined by sets of convergent sequences, J. Pure Appl. Algebra 217 (2013), 786-802.
    • (2013) J. Pure Appl. Algebra , vol.217 , pp. 786-802
    • Gabriyelyan, S.S.1
  • 28
    • 0001535687 scopus 로고
    • Uniform boundedness for groups
    • I. Glicksberg, Uniform boundedness for groups, Canad. J. Math. 14 (1962), 269-276.
    • (1962) Canad. J. Math. , vol.14 , pp. 269-276
    • Glicksberg, I.1
  • 29
    • 0001291052 scopus 로고
    • Free topological groups
    • (in Russian)
    • M. I. Graev, Free topological groups, Izv. Akad. Nauk SSSR Ser. Mat. 12 (1948), 279-324 (in Russian).
    • (1948) Izv. Akad. Nauk SSSR Ser. Mat. , vol.12 , pp. 279-324
    • Graev, M.I.1
  • 30
    • 18444400577 scopus 로고    scopus 로고
    • Limits in function spaces and compact groups
    • J. E. Hart and K. Kunen, Limits in function spaces and compact groups, Topology Appl. 151 (2005), 157-168.
    • (2005) Topology Appl. , vol.151 , pp. 157-168
    • Hart, J.E.1    Kunen, K.2
  • 31
    • 31844453685 scopus 로고    scopus 로고
    • Limits in compact abelian groups
    • J. E. Hart and K. Kunen, Limits in compact Abelian groups, Topology Appl. 153 (2006), 991-1002.
    • (2006) Topology Appl. , vol.153 , pp. 991-1002
    • Hart, J.E.1    Kunen, K.2
  • 32
    • 0038116903 scopus 로고    scopus 로고
    • Dual properties in totally bounded abelian groups
    • S. Hern'andez and S. Macario, Dual properties in totally bounded Abelian groups, Arch. Math. (Basel) 80 (2003), 271-283.
    • (2003) Arch. Math. (Basel) , vol.80 , pp. 271-283
    • Hern'Andez, S.1    MacArio, S.2
  • 34
    • 0037818466 scopus 로고
    • Coproducts of topological abelian groups
    • P. J. Higgins, Coproducts of topological abelian groups, J. Algebra 44 (1977), 152-159.
    • (1977) J. Algebra , vol.44 , pp. 152-159
    • Higgins, P.J.1
  • 35
    • 0041748299 scopus 로고    scopus 로고
    • Sequentially continuous homomorphisms on products of topological groups
    • M. Hu?sek, Sequentially continuous homomorphisms on products of topological groups, Topology Appl. 70 (1996), 155-165.
    • (1996) Topology Appl. , vol.70 , pp. 155-165
    • Husek, M.1
  • 36
    • 0000142226 scopus 로고
    • Extensions of the pontrjagin duality, i: Infinite products
    • S. Kaplan, Extensions of the Pontrjagin duality, I: Infinite products, Duke Math. J. 15 (1948), 649-658.
    • (1948) Duke Math. J. , vol.15 , pp. 649-658
    • Kaplan, S.1
  • 37
    • 0038495059 scopus 로고
    • Zur Dualit?atstheorie projektiver Limites abelscher Gruppen
    • H. Leptin, Zur Dualit?atstheorie projektiver Limites abelscher Gruppen, Abh. Math. Sem. Univ. Hamburg 19 (1955), 264-268.
    • (1955) Abh. Math. Sem. Univ. Hamburg , vol.19 , pp. 264-268
    • Leptin, H.1
  • 38
    • 33751337361 scopus 로고    scopus 로고
    • Precompact abelian groups and topological annihilators
    • G. Luk'acs, Precompact abelian groups and topological annihilators, J. Pure Appl. Algebra 208 (2007), 1159-1168.
    • (2007) J. Pure Appl. Algebra , vol.208 , pp. 1159-1168
    • Luk'Acs, G.1
  • 39
    • 0000716491 scopus 로고
    • On continuous mappings on cartesian products
    • S. Mazur, On continuous mappings on Cartesian products, Fund. Math. 39 (1952), 229-238.
    • (1952) Fund. Math. , vol.39 , pp. 229-238
    • Mazur, S.1
  • 40
    • 0038012871 scopus 로고    scopus 로고
    • Coproducts of abelian topological groups
    • P. Nickolas, Coproducts of abelian topological groups, Topology Appl. 120 (2002), 403-426.
    • (2002) Topology Appl. , vol.120 , pp. 403-426
    • Nickolas, P.1
  • 41
    • 0037836177 scopus 로고
    • Construction of group topologies on abelian groups
    • J. W. Nienhuys, Construction of group topologies on Abelian groups, Fund. Math. 75 (1972), 101-116.
    • (1972) Fund. Math. , vol.75 , pp. 101-116
    • Nienhuys, J.W.1
  • 42
    • 84966204069 scopus 로고
    • The continuity of functions on cartesian products
    • N. Noble, The continuity of functions on Cartesian products, Trans. Amer. Math. Soc. 149 (1970), 187-198.
    • (1970) Trans. Amer. Math. Soc. , vol.149 , pp. 187-198
    • Noble, N.1
  • 43
    • 0000067766 scopus 로고
    • K-groups and duality
    • N. Noble, k-groups and duality, Trans. Amer. Math. Soc. 151 (1970), 551-561.
    • (1970) Trans. Amer. Math. Soc. , vol.151 , pp. 551-561
    • Noble, N.1
  • 44
    • 84860833679 scopus 로고    scopus 로고
    • Maximal vector topologies
    • I. V. Protasov, Maximal vector topologies, Topology Appl. 159 (2012), 2510- 2512.
    • (2012) Topology Appl. , vol.159 , pp. 2510-2512
    • Protasov, I.V.1
  • 46
    • 0038496706 scopus 로고    scopus 로고
    • Totally bounded topological group topologies on the integers
    • S. U. Raczkowski, Totally bounded topological group topologies on the integers, Topology Appl. 121 (2002), 63-74.
    • (2002) Topology Appl. , vol.121 , pp. 63-74
    • Raczkowski, S.U.1
  • 47
    • 0003356198 scopus 로고
    • On sequential convergence in groups
    • G. A. Reid, On sequential convergence in groups, Math. Z. 102 (1967), 227-235.
    • (1967) Math. Z. , vol.102 , pp. 227-235
    • Reid, G.A.1
  • 48
    • 33751534455 scopus 로고    scopus 로고
    • Convergence in the presence of algebraic structure
    • North-Holland, Amsterdam
    • D. Shakhmatov, Convergence in the presence of algebraic structure, in: Recent Progress in General Topology, II, North-Holland, Amsterdam, 2002, 463-484.
    • (2002) Recent Progress in General Topology, II , pp. 463-484
    • Shakhmatov, D.1
  • 49
    • 0013496712 scopus 로고
    • Sequence-covering and countably bi-quotient mapping
    • F. Siwiec, Sequence-covering and countably bi-quotient mapping, General Topology Appl. 1 (1971), 143-154.
    • (1971) General Topology Appl. , vol.1 , pp. 143-154
    • Siwiec, F.1
  • 50
    • 84971124116 scopus 로고
    • A theorem on the continuity of homomorphisms of locally compact groups
    • N. Th. Varopoulos, A theorem on the continuity of homomorphisms of locally compact groups, Proc. Cambridge Philos. Soc. 60 (1964), 449-463.
    • (1964) Proc. Cambridge Philos. Soc. , vol.60 , pp. 449-463
    • Th. Varopoulos, N.1
  • 53
    • 0037818774 scopus 로고
    • Russian original
    • Russian original: Izv. Akad. Nauk SSSR Ser. Mat. 54 (1990), 1090-1107.
    • (1990) Izv. Akad. Nauk SSSR Ser. Mat. , vol.54 , pp. 1090-1107


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