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Volumn 159, Issue 3, 1999, Pages 195-218

The concept of boundedness and the bohr compactification of a MAP Abelian group

Author keywords

Bohr topology; Boundedness; C* embedded; C embedded; DF space; LCA group; Locally convex vector space; Maximally almost periodic; Respects compactness; group

Indexed keywords


EID: 0013503172     PISSN: 00162736     EISSN: None     Source Type: Journal    
DOI: 10.4064/fm-159-3-195-218     Document Type: Article
Times cited : (48)

References (35)
  • 1
    • 0003208315 scopus 로고
    • Additive subgroups of topological Vector spaces
    • Springer, Berlin
    • W. Banaszczyk, Additive Subgroups of Topological Vector Spaces, Lecture Notes in Math. 1466, Springer, Berlin, 1991.
    • (1991) Lecture Notes in Math , vol.1466
    • Banaszczyk, W.1
  • 2
    • 0009089358 scopus 로고    scopus 로고
    • The Glicksberg theorem on weakly compact sets for nuclear groups
    • W. Banaszczyk and E. Martín-Peinador, The Glicksberg Theorem on weakly compact sets for nuclear groups, Ann. New York Acad. Sci. 788 (1996), 34-39.
    • (1996) Ann. New York Acad. Sci. , vol.788 , pp. 34-39
    • Banaszczyk, W.1    Martín-Peinador, E.2
  • 3
    • 0030601036 scopus 로고    scopus 로고
    • Relating a locally compact Abelian group to its Bohr compactification
    • W. W. Comfort, S. Hernández 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    Hernández, S.2    Trigos-Arrieta, F.J.3
  • 4
    • 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
  • 5
    • 0011575516 scopus 로고
    • The Bohr compactification, modulo a metrizable subgroup
    • W. W. Comfort, F. J. Trigos-Arrieta, and T.-S. Wu, The Bohr compactification, modulo a metrizable subgroup, Fund. Math. 143 (1993), 119-136.
    • (1993) Fund. Math. , vol.143 , pp. 119-136
    • Comfort, W.W.1    Trigos-Arrieta, F.J.2    Wu, T.-S.3
  • 6
    • 0002432379 scopus 로고
    • The maximal totally bounded group topology on G and the biggest minimal G-space, for Abelian groups G
    • E. K. van Douwen, The maximal totally bounded group topology on G and the biggest minimal G-space, for Abelian groups G, Topology Appl. 34 (1990), 69-91.
    • (1990) Topology Appl. , vol.34 , pp. 69-91
    • Van Douwen, E.K.1
  • 10
    • 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
  • 11
    • 0037658193 scopus 로고
    • Almost periodic extensions of functions
    • S. Hartman and C. Ryll-Nardzewski, Almost periodic extensions of functions, Colloq. Math. 12 (1964), 29-39.
    • (1964) Colloq. Math. , vol.12 , pp. 29-39
    • Hartman, S.1    Ryll-Nardzewski, C.2
  • 12
    • 0038499502 scopus 로고
    • Almost periodic extensions of functions II
    • _, _, Almost periodic extensions of functions II, ibid. 15 (1966), 79-86.
    • (1966) Colloq. Math. , vol.15 , pp. 79-86
  • 13
    • 0039474969 scopus 로고
    • Boundedness in uniform spaces and topological groups
    • J. Hejcman, Boundedness in uniform spaces and topological groups, Czechoslovak Math. J. 9 (1962), 544-562.
    • (1962) Czechoslovak Math. J. , vol.9 , pp. 544-562
    • Hejcman, J.1
  • 14
  • 15
    • 84968518910 scopus 로고
    • Compactness in locally compact groups
    • R. Hughes, Compactness in locally compact groups, Bull. Amer. Math. Soc. 79 (1973), 122-123.
    • (1973) Bull. Amer. Math. Soc. , vol.79 , pp. 122-123
    • Hughes, R.1
  • 16
    • 0004002860 scopus 로고
    • Grundlehren Math. Wiss. 159, Springer, Berlin
    • G. Köthe, Topological Vector Spaces, Vol. I, Grundlehren Math. Wiss. 159, Springer, Berlin, 1969.
    • (1969) Topological Vector Spaces , vol.1
    • Köthe, G.1
  • 17
    • 0031470168 scopus 로고    scopus 로고
    • The free abelian topological group and the free locally convex space on the unit interval
    • A. G. Leiderman, S. A. Morris and V. G. Pestov, The free abelian topological group and the free locally convex space on the unit interval, J. London Math. Soc. 56 (1997), 529-538.
    • (1997) J. London Math. Soc. , vol.56 , pp. 529-538
    • Leiderman, A.G.1    Morris, S.A.2    Pestov, V.G.3
  • 18
    • 84974061285 scopus 로고
    • Uniform boundedness for non-abelian groups
    • M. Moskowitz, Uniform boundedness for non-abelian groups, Math. Proc. Cambridge Philos. Soc. 97 (1985), 107-110.
    • (1985) Math. Proc. Cambridge Philos. Soc. , vol.97 , pp. 107-110
    • Moskowitz, M.1
  • 19
    • 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
  • 20
    • 84973958483 scopus 로고
    • Free Abelian topological groups and the Pontryagin-van Kampen duality
    • V. Pestov, Free Abelian topological groups and the Pontryagin-van Kampen duality, Bull. Austral. Math. Soc. 52 (1995), 297-311.
    • (1995) Bull. Austral. Math. Soc. , vol.52 , pp. 297-311
    • Pestov, V.1
  • 21
    • 0000008090 scopus 로고
    • Abelian groups which satisfy Pontryagin duality need not respect compactness
    • D. Remus and F. J. Trigos-Arrieta, Abelian groups which satisfy Pontryagin duality need not respect compactness, Proc. Amer. Math. Soc. 117 (1993), 1195-1200.
    • (1993) Proc. Amer. Math. Soc. , vol.117 , pp. 1195-1200
    • Remus, D.1    Trigos-Arrieta, F.J.2
  • 22
    • 0037485755 scopus 로고
    • Concerning almost periodic extensions of functions
    • C. Ryll-Nardzewski, Concerning almost periodic extensions of functions, Colloq. Math. 12 (1964), 235-237.
    • (1964) Colloq. Math. , vol.12 , pp. 235-237
    • Ryll-Nardzewski, C.1
  • 23
    • 0013466905 scopus 로고
    • On countable inductive limits of locally compact abelian groups
    • L. J. Sulley, On countable inductive limits of locally compact abelian groups, J. London Math. Soc. (2) 5 (1972), 629-637.
    • (1972) J. London Math. Soc. , vol.5 , Issue.2 , pp. 629-637
    • Sulley, L.J.1
  • 24
    • 0000106052 scopus 로고
    • Completeness of free Abelian topological groups
    • in Russian
    • M. Tkachenko, Completeness of free Abelian topological groups, Dokl. Akad. Nauk SSSR 269 (1983), 299-303 (in Russian); English transl.: Soviet Math. Dokl. 27 (1983), 341-345.
    • (1983) Dokl. Akad. Nauk SSSR , vol.269 , pp. 299-303
    • Tkachenko, M.1
  • 25
    • 0000106052 scopus 로고
    • M. Tkachenko, Completeness of free Abelian topological groups, Dokl. Akad. Nauk SSSR 269 (1983), 299-303 (in Russian); English transl.: Soviet Math. Dokl. 27 (1983), 341-345.
    • (1983) Soviet Math. Dokl. , vol.27 , pp. 341-345
  • 26
    • 0000536334 scopus 로고
    • Continuity, boundedness, connectedness and the Lindelöf property for topological groups
    • F. J. Trigos-Arrieta, Continuity, boundedness, connectedness and the Lindelöf property for topological groups, J. Pure Appl. Algebra 70 (1991), 199-210.
    • (1991) J. Pure Appl. Algebra , vol.70 , pp. 199-210
    • Trigos-Arrieta, F.J.1
  • 27
    • 0041057533 scopus 로고
    • On the topology of a free locally convex space
    • in Russian
    • V. V. Uspenskiǐ, On the topology of a free locally convex space, Dokl. Akad. Nauk SSSR 270 (1983), 1334-1337 (in Russian); English transl.: Soviet Math. Dokl. 27 (1983), 781-785.
    • (1983) Dokl. Akad. Nauk SSSR , vol.270 , pp. 1334-1337
    • Uspenskiǐ, V.V.1
  • 28
    • 0010668248 scopus 로고
    • V. V. Uspenskiǐ, On the topology of a free locally convex space, Dokl. Akad. Nauk SSSR 270 (1983), 1334-1337 (in Russian); English transl.: Soviet Math. Dokl. 27 (1983), 781-785.
    • (1983) Soviet Math. Dokl. , vol.27 , pp. 781-785
  • 29
    • 0037865275 scopus 로고
    • Free topological groups of metrizable spaces
    • in Russian
    • _, Free topological groups of metrizable spaces, Izv. Akad. Nauk SSSR Ser. Mat. 54 (1990), 1295-1319 (in Russian); English transl.: Math. USSR-Izv. 37 (1991), 657-680.
    • (1990) Izv. Akad. Nauk SSSR Ser. Mat. , vol.54 , pp. 1295-1319
  • 30
    • 0001239842 scopus 로고
    • _, Free topological groups of metrizable spaces, Izv. Akad. Nauk SSSR Ser. Mat. 54 (1990), 1295-1319 (in Russian); English transl.: Math. USSR-Izv. 37 (1991), 657-680.
    • (1991) Math. USSR-Izv. , vol.37 , pp. 657-680
  • 31
    • 0040066720 scopus 로고
    • r-complete
    • r-complete, Math. Ann. 211 (1974), 145-149.
    • (1974) Math. Ann. , vol.211 , pp. 145-149
    • Valdivia, M.1
  • 32
    • 84931121031 scopus 로고
    • r-complete
    • r-complete, Ann. Inst. Fourier (Grenoble) 27 (1977), no. 4, 29-43.
    • (1977) Ann. Inst. Fourier (Grenoble) , vol.27 , Issue.4 , pp. 29-43
  • 35
    • 0040271568 scopus 로고
    • Theory of characters of topological Abelian groups with a given boundedness
    • in Russian
    • N. Ya. Vilenkin, Theory of characters of topological Abelian groups with a given boundedness, Izv. Akad. Nauk SSSR Ser. Mat. 15 (1951), 439-462 (in Russian).
    • (1951) Izv. Akad. Nauk SSSR Ser. Mat. , vol.15 , pp. 439-462
    • Vilenkin, N.Ya.1


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