메뉴 건너뛰기




Volumn 120, Issue 2, 1996, Pages 322-344

Relating a locally compact Abelian group to its Bohr compactification

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0030601036     PISSN: 00018708     EISSN: None     Source Type: Journal    
DOI: 10.1006/aima.1996.0042     Document Type: Article
Times cited : (24)

References (68)
  • 1
    • 0001464247 scopus 로고
    • A note on compact representations and almost periodicity in topological groups
    • 1. E. M. ALFSEN AND P. HOLM, A note on compact representations and almost periodicity in topological groups, Math. Scand. 10 (1962), 127-136.
    • (1962) Math. Scand. , vol.10 , pp. 127-136
    • Alfsen, E.M.1    Holm, P.2
  • 2
    • 0011570387 scopus 로고
    • Bohr compactifications of a locally compact Abelian group, I
    • 2. H. ANZAI AND S. KAKUTANI, Bohr compactifications of a locally compact Abelian group, I, Proc. Imperial Acad. Tokyo 19 (1943), 476-480.
    • (1943) Proc. Imperial Acad. Tokyo , vol.19 , pp. 476-480
    • Anzai, H.1    Kakutani, S.2
  • 3
    • 0000961821 scopus 로고
    • Spaces in which special sets are z-embedded
    • 3. R. L. BLAIR, Spaces in which special sets are z-embedded, Canad. J. Math. 28 (1976), 673-690.
    • (1976) Canad. J. Math. , vol.28 , pp. 673-690
    • Blair, R.L.1
  • 4
    • 0001771066 scopus 로고
    • Extensions of zero-sets and of real-valued continuous functions
    • 4. R. L. BLAIR AND A. W. HAGER, Extensions of zero-sets and of real-valued continuous functions, Math. Z. 136 (1974), 41-52.
    • (1974) Math. Z. , vol.136 , pp. 41-52
    • Blair, R.L.1    Hager, A.W.2
  • 5
    • 0001854919 scopus 로고
    • Topological groups
    • (Kenneth Kunen and Jerry E. Vaughan, Eds.), North-Holland, Amsterdam
    • 5. W. W. COMFORT, Topological groups, in "Handbook of Set-theoretic Topology" (Kenneth Kunen and Jerry E. Vaughan, Eds.), pp. 1143-1263, North-Holland, Amsterdam, 1984.
    • (1984) Handbook of Set-Theoretic Topology , pp. 1143-1263
    • Comfort, W.W.1
  • 6
    • 0001771807 scopus 로고
    • Topological groups and semigroups
    • (M. Hušek and J. van Mill, Eds.), Elsevier, Amsterdam
    • 6. W. W. COMFORT, K.-H. HOFMANN, AND D. REMUS, Topological groups and semigroups, in "Recent Progress in General Topology" (M. Hušek and J. van Mill, Eds.), pp. 59-144, Elsevier, Amsterdam, 1992.
    • (1992) Recent Progress in General Topology , pp. 59-144
    • Comfort, W.W.1    Hofmann, K.-H.2    Remus, D.3
  • 8
  • 9
    • 0011575516 scopus 로고
    • The Bohr compactification, modulo a metrizable subgroup
    • 9. W. W. COMFORT, F. J. TRIGOS-ARRIETA, AND T.-S. WU, The Bohr compactification, modulo a metrizable subgroup, Fund. Math. (1993), 119-136.
    • (1993) Fund. Math. , pp. 119-136
    • Comfort, W.W.1    Trigos-Arrieta, F.J.2    Wu, T.-S.3
  • 10
    • 0002473421 scopus 로고
    • Remarks on a theorem of Glicksberg
    • (S. J. Andima, R. Kopperman, P. R. Misra, J. Z. Reichman, and A. R. Todd, Eds.), Dekker, New York/Basel/Hong Kong
    • 10. W. W. COMFORT AND F. JAVIER TRIGOS-ARRIETA, Remarks on a theorem of Glicksberg, in "General Topology and Applications" (S. J. Andima, R. Kopperman, P. R. Misra, J. Z. Reichman, and A. R. Todd, Eds.), pp. 25-33, Dekker, New York/Basel/Hong Kong, 1991.
    • (1991) General Topology and Applications , pp. 25-33
    • Comfort, W.W.1    Javier Trigos-Arrieta, F.2
  • 11
    • 84968469717 scopus 로고
    • The weak topology of a Banach space
    • 11. H. H. CORSON, The weak topology of a Banach space, Trans. Amer. Math. Soc. 101 (1961), 1-15.
    • (1961) Trans. Amer. Math. Soc. , vol.101 , pp. 1-15
    • Corson, H.H.1
  • 14
    • 0002432379 scopus 로고
    • The maximal totally bounded group topology on G and the biggest minimal G-space for Abelian groups G
    • 14. 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
  • 16
    • 0001631623 scopus 로고
    • Extending continuous functions on zero-dimensional spaces
    • 16. R. L. ELLIS, Extending continuous functions on zero-dimensional spaces, Math. Ann. 186 (1970), 114-122.
    • (1970) Math. Ann. , vol.186 , pp. 114-122
    • Ellis, R.L.1
  • 18
    • 0000216378 scopus 로고
    • Zur Bohr-Konvergenz der folgen
    • 18. P. FLOR, Zur Bohr-Konvergenz der Folgen, Math. Scand. 23 (1968), 169-170.
    • (1968) Math. Scand. , vol.23 , pp. 169-170
    • Flor, P.1
  • 19
    • 0000753510 scopus 로고
    • Applications of complete families of functions to the theory of Q-spaces
    • in English, Russian summary
    • 19. Z. FROLÍK, Applications of complete families of functions to the theory of Q-spaces, Czech. Math. J. 11 (1961), 115-133 [in English, Russian summary].
    • (1961) Czech. Math. J. , vol.11 , pp. 115-133
    • Frolík, Z.1
  • 20
    • 0003939143 scopus 로고
    • Academic Press, New York/San Francisco/London
    • 20. L. FUCHS, "Infinite Abelian Groups," Academic Press, New York/San Francisco/London, 1970.
    • (1970) Infinite Abelian Groups
    • Fuchs, L.1
  • 23
    • 0001535687 scopus 로고
    • Uniform boundedness for groups
    • 23. 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
  • 24
    • 84963108536 scopus 로고
    • On inverse-closed subalgebras of C(X)
    • 24. A. W. HAGER, On inverse-closed subalgebras of C(X), Proc. London Math. Soc. 19 (1969), 233-257.
    • (1969) Proc. London Math. Soc. , vol.19 , pp. 233-257
    • Hager, A.W.1
  • 25
    • 0001787364 scopus 로고
    • Discrete sets and the maximal totally bounded group topology
    • 25. K. P. HART AND J. VAN MILL, Discrete sets and the maximal totally bounded group topology, J. Pure Appl. Algebra 70 (1991), 73-80.
    • (1991) J. Pure Appl. Algebra , vol.70 , pp. 73-80
    • Hart, K.P.1    Van Mill, J.2
  • 26
    • 0011576316 scopus 로고
    • On compactness in spaces of measures and measurecompact spaces
    • 26. R. HAYDON, On compactness in spaces of measures and measurecompact spaces, Proc. London Math. Soc. 29 (1974), 1-16.
    • (1974) Proc. London Math. Soc. , vol.29 , pp. 1-16
    • Haydon, R.1
  • 27
    • 0002127181 scopus 로고
    • On the structure of the class of archimedean lattice-ordered algebras
    • 27. M. HENRIKSEN AND D. G. JOHNSON, On the structure of the class of archimedean lattice-ordered algebras, Fund. Math. 50 (1961), 73-94.
    • (1961) Fund. Math. , vol.50 , pp. 73-94
    • Henriksen, M.1    Johnson, D.G.2
  • 28
    • 38248998760 scopus 로고
    • δ-open functionally bounded subsets in topological groups
    • δ-open functionally bounded subsets in topological groups, Topology Appl. 53 (1993), 289-299.
    • (1993) Topology Appl. , vol.53 , pp. 289-299
    • Hernández, S.1    Sanchis, M.2
  • 29
    • 84935154381 scopus 로고
    • Rings of real-valued continuous functions, I
    • 29. E. HEWITT, Rings of real-valued continuous functions, I, Trans. Amer. Math. Soc. 64 (1948), 45-99.
    • (1948) Trans. Amer. Math. Soc. , vol.64 , pp. 45-99
    • Hewitt, E.1
  • 33
    • 4944248971 scopus 로고
    • Dualität lokalkompakter gruppen
    • Springer-Verlag, Berlin/Heidelberg/New York
    • 33. H. HEYER, "Dualität lokalkompakter Gruppen," Lecture Notes in Mathematics, Vol. 150, Springer-Verlag, Berlin/Heidelberg/New York, 1970.
    • (1970) Lecture Notes in Mathematics , vol.150
    • Heyer, H.1
  • 34
    • 84968518910 scopus 로고
    • Compactness in locally compact groups
    • 34. 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
  • 35
    • 0002742863 scopus 로고
    • Algebras of uniformly continuous functions
    • 35. J. R. ISBELL, Algebras of uniformly continuous functions, Ann. of Math. 68 (1958), 96-125.
    • (1958) Ann. of Math. , vol.68 , pp. 96-125
    • Isbell, J.R.1
  • 36
    • 0011697893 scopus 로고
    • On the density character of compact topological groups
    • 36. G. L. ITZKOWITZ, On the density character of compact topological groups, Fund. Math. 75 (1972), 201-203.
    • (1972) Fund. Math. , vol.75 , pp. 201-203
    • Itzkowitz, G.L.1
  • 37
    • 0001233969 scopus 로고
    • On cardinal numbers related with a compact group
    • 37. S. KAKUTANI, On cardinal numbers related with a compact group, Proc. Imperial Acad. Tokyo 19 (1943), 366-372.
    • (1943) Proc. Imperial Acad. Tokyo , vol.19 , pp. 366-372
    • Kakutani, S.1
  • 38
    • 0000925071 scopus 로고
    • Über das haarsche mass in der lokal bikompacten gruppen
    • 38. S. KAKUTANI AND K. KODAIRA, Über das Haarsche Mass in der lokal bikompacten Gruppen, Proc. Imperial Acad. Tokyo 20 (1944), 444-450.
    • (1944) Proc. Imperial Acad. Tokyo , vol.20 , pp. 444-450
    • Kakutani, S.1    Kodaira, K.2
  • 39
    • 84972557915 scopus 로고
    • Some topological properties of spaces of measures
    • 39. G. KOUMOULLIS, Some topological properties of spaces of measures, Pacific J. Math. 96 (1981), 419-433.
    • (1981) Pacific J. Math. , vol.96 , pp. 419-433
    • Koumoullis, G.1
  • 40
    • 0011635120 scopus 로고
    • Equivalence of a problem in a measure theory to a problem in the theory of vector lattices
    • 40. G. W. MACKEY, Equivalence of a problem in a measure theory to a problem in the theory of vector lattices, Bull. Amer. Math. Soc. 50 (1944), 719-722.
    • (1944) Bull. Amer. Math. Soc. , vol.50 , pp. 719-722
    • Mackey, G.W.1
  • 41
    • 84966200846 scopus 로고
    • The product of a normal space and a metric space need not be normal
    • 41. E. MICHAEL, The product of a normal space and a metric space need not be normal, Bull. Amer. Math. Soc. 69 (1963), 375-376.
    • (1963) Bull. Amer. Math. Soc. , vol.69 , pp. 375-376
    • Michael, E.1
  • 42
    • 0011571251 scopus 로고
    • On almost periodic compactifications of locally compact groups
    • 42. W. MORAN, On almost periodic compactifications of locally compact groups, J. London Math. Soc. (2) 3 (1971), 507-512.
    • (1971) J. London Math. Soc. (2) , vol.3 , pp. 507-512
    • Moran, W.1
  • 43
    • 84968480677 scopus 로고
    • Almost periodic functions in a group, I
    • 43. J. VON NEUMANN, Almost periodic functions in a group, I, Trans. Amer. Math. Soc. 36 (1934), 445-492.
    • (1934) Trans. Amer. Math. Soc. , vol.36 , pp. 445-492
    • Von Neumann, J.1
  • 44
  • 45
    • 0000067766 scopus 로고
    • k-groups and duality
    • 45. 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
  • 46
    • 84966207253 scopus 로고
    • C-embedded subsets of products
    • 46. N. NOBLE, C-embedded subsets of products, Proc. Amer. Math. Soc. 31 (1972), 613-614.
    • (1972) Proc. Amer. Math. Soc. , vol.31 , pp. 613-614
    • Noble, N.1
  • 47
    • 0011635121 scopus 로고
    • Open mappings of normal spaces
    • 47. V. I. PONOMAREV, Open mappings of normal spaces, Dokl. Acad. Nauk. SSSR 126 (1959), 716-718.
    • (1959) Dokl. Acad. Nauk. SSSR , vol.126 , pp. 716-718
    • Ponomarev, V.I.1
  • 48
    • 0003356198 scopus 로고
    • On sequential convergence in groups
    • 48. G. A. REID, On sequential convergence in groups, Math. Z. 102 (1967), 225-235.
    • (1967) Math. Z. , vol.102 , pp. 225-235
    • Reid, G.A.1
  • 49
    • 0000008090 scopus 로고
    • Abelian groups which satisfy Pontryagin duality need not respect compactness
    • 49. 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
  • 50
    • 0011639896 scopus 로고
    • Baire sets and Baire measures
    • 50. K. A. ROSS AND K. R. STROMBERG, Baire sets and Baire measures, Ark. Mat. 6 (1967), 151-160.
    • (1967) Ark. Mat. , vol.6 , pp. 151-160
    • Ross, K.A.1    Stromberg, K.R.2
  • 51
    • 0011623667 scopus 로고
    • On topological products, groups, and a new class of spaces more general than metric spaces
    • 51. E. V. ŠČEPIN, On topological products, groups, and a new class of spaces more general than metric spaces, Soviet Math. Dokl. 17 (1976), 152-155; Dokl. Akad. Nauk SSSR 226 (1976), 527-529 [Russian original].
    • (1976) Soviet Math. Dokl. , vol.17 , pp. 152-155
    • Ščepin, E.V.1
  • 52
    • 0011570389 scopus 로고
    • Russian original
    • 51. E. V. ŠČEPIN, On topological products, groups, and a new class of spaces more general than metric spaces, Soviet Math. Dokl. 17 (1976), 152-155; Dokl. Akad. Nauk SSSR 226 (1976), 527-529 [Russian original].
    • (1976) Dokl. Akad. Nauk SSSR , vol.226 , pp. 527-529
  • 53
    • 84956067105 scopus 로고
    • On κ-metrizable spaces
    • 52. E. V. ŠČEPIN, On κ-metrizable spaces, Math. USSR Izv. 14 (1980), 407-440; Izv. Akad. Nauk SSSR Soc. Mat. 43 (1979), 442-478 [Russian original].
    • (1980) Math. USSR Izv. , vol.14 , pp. 407-440
    • Ščepin, E.V.1
  • 54
    • 84956067105 scopus 로고
    • Russian original
    • 52. E. V. ŠČEPIN, On κ-metrizable spaces, Math. USSR Izv. 14 (1980), 407-440; Izv. Akad. Nauk SSSR Soc. Mat. 43 (1979), 442-478 [Russian original].
    • (1979) Izv. Akad. Nauk SSSR Soc. Mat. , vol.43 , pp. 442-478
  • 55
    • 38249020179 scopus 로고
    • Imbeddings into topological groups preserving dimensions
    • 53. D. B. SHAKHMATOV, Imbeddings into topological groups preserving dimensions, Topology Appl. 36 (1990), 181-204.
    • (1990) Topology Appl. , vol.36 , pp. 181-204
    • Shakhmatov, D.B.1
  • 56
    • 0011572133 scopus 로고
    • A survey of current researches and open problems in the dimension theory of topological groups, Q&A
    • 54. D. B. SHAKHMATOV, A survey of current researches and open problems in the dimension theory of topological groups, Q&A, General Topology 8 (1990), 101-128.
    • (1990) General Topology , vol.8 , pp. 101-128
    • Shakhmatov, D.B.1
  • 57
    • 0011570085 scopus 로고
    • The notion of o-tightness and C-embedded subspaces of products
    • 55. M. G. TKAČENKO, The notion of o-tightness and C-embedded subspaces of products, Topology Appl. 15 (1983), 93-98.
    • (1983) Topology Appl. , vol.15 , pp. 93-98
    • Tkačenko, M.G.1
  • 58
    • 0011623668 scopus 로고
    • Factorization theorems for topological groups and their applications
    • 56. M. G. TKAČHENKO, Factorization theorems for topological groups and their applications, Topology Appl. 38 (1991), 21-37.
    • (1991) Topology Appl. , vol.38 , pp. 21-37
    • Tkačhenko, M.G.1
  • 60
    • 0000536334 scopus 로고
    • Continuity, boundedness, connectedness and the Lindelöf property for topological groups
    • 58. 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
  • 61
    • 84966246426 scopus 로고
    • Every uncountable Abelian group admits a non-normal group topology
    • 59. F. J. TRIGOS-ARRIETA, Every uncountable Abelian group admits a non-normal group topology, Proc. Amer. Math. Soc. 122 (1994), 907-909.
    • (1994) Proc. Amer. Math. Soc. , vol.122 , pp. 907-909
    • Trigos-Arrieta, F.J.1
  • 62
    • 85029961787 scopus 로고
    • Normality and the weak topology on a locally compact Abelian group
    • "Papers on General Topology and Applications. Proc. Queens College Summer Conference on General Topology and Applications, June 1992," (S. Andima, G. Itzkowitz, T. Y. Kong, R. Kopperman, P. R. Misa, and A. Todd, Eds.), New York Academy of Science, New York
    • 60. F. JAVIER TRIGOS-ARRIETA, Normality and the weak topology on a locally compact Abelian group, in "Papers on General Topology and Applications, Proc. Queens College Summer Conference on General Topology and Applications, June 1992," Annals of the New York Academy of Sciences, Vol. 728 (S. Andima, G. Itzkowitz, T. Y. Kong, R. Kopperman, P. R. Misa, and A. Todd, Eds.), pp. 237-247, New York Academy of Science, New York, 1994.
    • (1994) Annals of the New York Academy of Sciences , vol.728 , pp. 237-247
    • Javier Trigos-Arrieta, F.1
  • 63
    • 84971124116 scopus 로고
    • A theorem on the continuity of homomorphisms of locally compact groups
    • 61. 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
    • Varopoulos, N.Th.1
  • 65
    • 0000805025 scopus 로고
    • Stetigkeitssätze für halbeinfache Liesche gruppen
    • 63. B. L. VAN DER WAERDEN, Stetigkeitssätze für halbeinfache Liesche Gruppen, Math. Z. 36 (1933), 780-786.
    • (1933) Math. Z. , vol.36 , pp. 780-786
    • Van Der Waerden, B.L.1
  • 67
    • 0011573294 scopus 로고
    • Weak and pointwise compactness in the space of bounded continuous functions
    • 65. R. F. WHEELER, Weak and pointwise compactness in the space of bounded continuous functions, Trans. Amer. Math. Soc. 266 (1981), 515-530.
    • (1981) Trans. Amer. Math. Soc. , vol.266 , pp. 515-530
    • Wheeler, R.F.1
  • 68
    • 0002272261 scopus 로고
    • A survey of Baire measures and strict topologies
    • 66. R. F. WHEELER, A survey of Baire measures and strict topologies, Expositiones Math. 2 (1983), 87-190.
    • (1983) Expositiones Math. , vol.2 , pp. 87-190
    • Wheeler, R.F.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.