메뉴 건너뛰기




Volumn 226, Issue 6, 2011, Pages 4776-4795

A Kronecker-Weyl theorem for subsets of abelian groups

Author keywords

Bohr compactification; Bohr topology; Diophantine approximation; Discrete flow; Markov problem; Potentially dense set; Primary; Secondary; Uniform distribution; Weyl criterion; Zariski closure; Zariski topology

Indexed keywords


EID: 79952037927     PISSN: 00018708     EISSN: 10902082     Source Type: Journal    
DOI: 10.1016/j.aim.2010.12.016     Document Type: Article
Times cited : (11)

References (25)
  • 1
    • 0033196988 scopus 로고    scopus 로고
    • Algebraic geometry over groups, I. Algebraic sets and ideal theory
    • Baumslag G., Myasnikov A., Remeslennikov V. Algebraic geometry over groups, I. Algebraic sets and ideal theory. J. Algebra 1999, 219:16-79.
    • (1999) J. Algebra , vol.219 , pp. 16-79
    • Baumslag, G.1    Myasnikov, A.2    Remeslennikov, V.3
  • 2
    • 0013479039 scopus 로고
    • Dansk Matemetitisk Forsening, E. Føelner, B. Jessen (Eds.)
    • Bohr H. Collected Mathematical Works 1952, Dansk Matemetitisk Forsening. E. Føelner, B. Jessen (Eds.).
    • (1952) Collected Mathematical Works
    • Bohr, H.1
  • 3
    • 0000901540 scopus 로고
    • The verbal topology of a group
    • Bryant R. The verbal topology of a group. J. Algebra 1977, 48:340-346.
    • (1977) J. Algebra , vol.48 , pp. 340-346
    • Bryant, R.1
  • 4
    • 84972570839 scopus 로고
    • Countably compact groups and finest totally bounded topologies
    • Comfort W., Saks V. Countably compact groups and finest totally bounded topologies. Pacific J. Math. 1973, 49:33-44.
    • (1973) Pacific J. Math. , vol.49 , pp. 33-44
    • Comfort, W.1    Saks, V.2
  • 5
    • 0002473421 scopus 로고
    • Remarks on a theorem of Glicksberg
    • Dekker, New York, General Topology and Applications
    • Comfort W., Trigos-Arrieta J. Remarks on a theorem of Glicksberg. Lect. Notes Pure Appl. Math. 1991, vol. 134:25-33. Dekker, New York.
    • (1991) Lect. Notes Pure Appl. Math. , vol.134 , pp. 25-33
    • Comfort, W.1    Trigos-Arrieta, J.2
  • 7
    • 18444378751 scopus 로고    scopus 로고
    • Forcing hereditarily separable compact-like group topologies on Abelian groups
    • Dikranjan D., Shakhmatov D. Forcing hereditarily separable compact-like group topologies on Abelian groups. Topology Appl. 2005, 151:2-54.
    • (2005) Topology Appl. , vol.151 , pp. 2-54
    • Dikranjan, D.1    Shakhmatov, D.2
  • 8
    • 77952041753 scopus 로고    scopus 로고
    • Hewitt-Marczewski-Pondiczery type theorem for abelian groups and Markov's potential density
    • Dikranjan D., Shakhmatov D. Hewitt-Marczewski-Pondiczery type theorem for abelian groups and Markov's potential density. Proc. Amer. Math. Soc. 2010, 138:2979-2990.
    • (2010) Proc. Amer. Math. Soc. , vol.138 , pp. 2979-2990
    • Dikranjan, D.1    Shakhmatov, D.2
  • 9
    • 44349164397 scopus 로고    scopus 로고
    • Reflection principle characterizing groups in which unconditionally closed sets are algebraic
    • Dikranjan D., Shakhmatov D. Reflection principle characterizing groups in which unconditionally closed sets are algebraic. J. Group Theory 2008, 11:421-442.
    • (2008) J. Group Theory , vol.11 , pp. 421-442
    • Dikranjan, D.1    Shakhmatov, D.2
  • 10
    • 77950825980 scopus 로고    scopus 로고
    • Selected topics from the structure theory of topological groups
    • Elsevier, E. Pearl (Ed.)
    • Dikranjan D., Shakhmatov D. Selected topics from the structure theory of topological groups. Open Problems in Topology II 2007, 389-406. Elsevier. E. Pearl (Ed.).
    • (2007) Open Problems in Topology II , pp. 389-406
    • Dikranjan, D.1    Shakhmatov, D.2
  • 11
    • 77955303877 scopus 로고    scopus 로고
    • The Markov-Zariski topology of an abelian group
    • Dikranjan D., Shakhmatov D. The Markov-Zariski topology of an abelian group. J. Algebra 2010, 324:1125-1158.
    • (2010) J. Algebra , vol.324 , pp. 1125-1158
    • Dikranjan, D.1    Shakhmatov, D.2
  • 12
    • 0242298183 scopus 로고    scopus 로고
    • Algebraic structure of small countably compact Abelian groups
    • Dikranjan D., Tkachenko M. Algebraic structure of small countably compact Abelian groups. Forum Math. 2003, 15:811-837.
    • (2003) Forum Math. , vol.15 , pp. 811-837
    • Dikranjan, D.1    Tkachenko, M.2
  • 13
    • 0005631115 scopus 로고    scopus 로고
    • Weakly complete free topological groups
    • Dikranjan D., Tkachenko M. Weakly complete free topological groups. Topology Appl. 2001, 112:259-287.
    • (2001) Topology Appl. , vol.112 , pp. 259-287
    • Dikranjan, D.1    Tkachenko, M.2
  • 14
    • 0003360246 scopus 로고
    • General Topology
    • Heldermann Verlag, Berlin
    • Engel'king R. General Topology. Sigma Ser. Pure Math. 1989, vol. 6. Heldermann Verlag, Berlin. second ed.
    • (1989) Sigma Ser. Pure Math. , vol.6
    • Engel'king, R.1
  • 15
    • 0000216378 scopus 로고
    • Zur Bohr-Konvergenz von Folgen
    • Flor P. Zur Bohr-Konvergenz von Folgen. Math. Scand. 1968, 23:169-170.
    • (1968) Math. Scand. , vol.23 , pp. 169-170
    • Flor, P.1
  • 17
    • 0001535687 scopus 로고
    • Uniform boundedness for groups
    • Glicksberg I. Uniform boundedness for groups. Canad. J. Math. 1962, 14:269-276.
    • (1962) Canad. J. Math. , vol.14 , pp. 269-276
    • Glicksberg, I.1
  • 18
    • 84935154381 scopus 로고
    • Rings of real-valued continuous functions I
    • Hewitt E. Rings of real-valued continuous functions I. Trans. Amer. Math. Soc. 1948, 64:45-99.
    • (1948) Trans. Amer. Math. Soc. , vol.64 , pp. 45-99
    • Hewitt, E.1
  • 19
    • 0242384515 scopus 로고
    • On unconditionally closed sets
    • (in Russian)
    • Markov A.A. On unconditionally closed sets. C. R. Dokl. AN SSSR (N.S.) 1944, 44:180-181. (in Russian).
    • (1944) C. R. Dokl. AN SSSR (N.S.) , vol.44 , pp. 180-181
    • Markov, A.A.1
  • 20
    • 0038413198 scopus 로고
    • On unconditionally closed sets
    • (in Russian); English translation in: A.A. Markov, Three papers on topological groups: I. On the existence of periodic connected topological groups, II. On free topological groups, III. On unconditionally closed sets, Amer. Math. Soc. Transl., vol. 1950, 1950, No. 30, 120 pp.; yet another English translation in:, Amer. Math. Soc.
    • Markov A.A. On unconditionally closed sets. Mat. Sb.. Topology Topol. Algebra Transl. Ser. 1 1962, vol. 8:273-304. (in Russian); English translation in: A.A. Markov, Three papers on topological groups: I. On the existence of periodic connected topological groups, II. On free topological groups, III. On unconditionally closed sets, Amer. Math. Soc. Transl., vol. 1950, 1950, No. 30, 120 pp.; yet another English translation in:, Amer. Math. Soc.
    • (1962) Mat. Sb.. Topology Topol. Algebra Transl. Ser. 1 , vol.8 , pp. 273-304
    • Markov, A.A.1
  • 21
    • 18444381299 scopus 로고
    • Sur la puissance d'un espace contenant une partie dense de puissance donnée
    • Pospíšil B. Sur la puissance d'un espace contenant une partie dense de puissance donnée. časopis Pro Pěstování Matematiky a Fysiky 1937, 67:89-96.
    • (1937) časopis Pro Pěstování Matematiky a Fysiky , vol.67 , pp. 89-96
    • Pospíšil, B.1
  • 22
    • 0038688709 scopus 로고    scopus 로고
    • Independent group topologies on Abelian groups
    • Tkachenko M., Yaschenko I. Independent group topologies on Abelian groups. Topology Appl. 2002, 122:425-451.
    • (2002) Topology Appl. , vol.122 , pp. 425-451
    • Tkachenko, M.1    Yaschenko, I.2
  • 23
    • 0002432379 scopus 로고
    • The maximal totally bounded group topology on G and the biggest minimal G-space for Abelian groups G
    • van Douwen E.K. The maximal totally bounded group topology on G and the biggest minimal G-space for Abelian groups G. Topology Appl. 1990, 34:69-91.
    • (1990) Topology Appl. , vol.34 , pp. 69-91
    • van Douwen, E.K.1
  • 25
    • 0037960194 scopus 로고
    • Über die Gleichverteilung von Zahlen mod. Eins
    • Weyl H. Über die Gleichverteilung von Zahlen mod. Eins. Math. Ann. 1916, 77(3):313-352.
    • (1916) Math. Ann. , vol.77 , Issue.3 , pp. 313-352
    • Weyl, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.