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Volumn 8, Issue 1, 2018, Pages

Separability of topological groups: A survey with open problems

Author keywords

Free topological group; Isomorphic embedding; Product; Quotient group; Separable topological group; Subgroup

Indexed keywords


EID: 85060584240     PISSN: None     EISSN: 20751680     Source Type: Journal    
DOI: 10.3390/axioms8010003     Document Type: Article
Times cited : (7)

References (41)
  • 1
    • 85044957534 scopus 로고    scopus 로고
    • Products of topological groups in which all closed subgroups are separable
    • Leiderman, A.G.; Tkachenko, M.G. Products of topological groups in which all closed subgroups are separable. Topol. Appl. 2018, 241, 89-101
    • (2018) Topol. Appl , vol.241 , pp. 89-101
    • Leiderman, A.G.1    Tkachenko, M.G.2
  • 3
    • 84954460567 scopus 로고    scopus 로고
    • Nonseparable closed vector subspaces of separable topological vector spaces
    • Erratum in 2017;182:49-50
    • Kakol, J.; Leiderman, A.G.; Morris, S.A. Nonseparable closed vector subspaces of separable topological vector spaces. Monatsh. Math. 2017, 182, 39-47; Erratum in 2017, 182, 49-50
    • (2017) Monatsh. Math , vol.182 , pp. 39-47
    • Kakol, J.1    Leiderman, A.G.2    Morris, S.A.3
  • 6
    • 85060582823 scopus 로고    scopus 로고
    • Topological groups whose closed subgroups are separable and the product operation
    • to appear
    • Xiao, Z.; Sánchez, I.; Tkachenko, M. Topological groups whose closed subgroups are separable and the product operation. Topol. Appl. 2019, to appear
    • (2019) Topol. Appl
    • Xiao, Z.1    Sánchez, I.2    Tkachenko, M.3
  • 7
    • 85060598070 scopus 로고    scopus 로고
    • A topological group observation on the Banach-Mazur separable quotient problem
    • to appear
    • Gabriyelyan, S.S.; Morris, S.A. A topological group observation on the Banach-Mazur separable quotient problem. Topol. Appl. 2019, to appear
    • (2019) Topol. Appl
    • Gabriyelyan, S.S.1    Morris, S.A.2
  • 8
    • 84869220230 scopus 로고    scopus 로고
    • Continuous isomorphisms onto separable groups
    • López, L.F.M. Continuous isomorphisms onto separable groups. Appl. Gen. Topol. 2012, 13, 135-150
    • (2012) Appl. Gen. Topol , vol.13 , pp. 135-150
    • López, L.F.M.1
  • 9
    • 0003798198 scopus 로고
    • Heldermann Verlag: Berlin, Germany
    • Engelking, R. General Topology; Heldermann Verlag: Berlin, Germany, 1989
    • (1989) General Topology
    • Engelking, R.1
  • 10
    • 64049104305 scopus 로고    scopus 로고
    • Atlantis Series in Mathematics; Atlantis Press and World Scientific: Paris, France; Amsterdam, The Netherlands
    • Arhangel'skii, A.V.; Tkachenko, M.G. Topological Groups and Related Structures; Atlantis Series in Mathematics, Volume I; Atlantis Press and World Scientific: Paris, France; Amsterdam, The Netherlands, 2008
    • (2008) Topological Groups and Related Structures , vol.1
    • Arhangel'skii, A.V.1    Tkachenko, M.G.2
  • 11
    • 85060658828 scopus 로고
    • Cardinal Functions I, Chapter 1
    • Kunen, K., Vaughan, J.E., Eds.; North Holland: Amsterdam, The Netherlands; New York, NY, USA; Oxford, UK
    • Hodel, R.E. Cardinal Functions I, Chapter 1. In Handbook of Set-Theoretic Topology; Kunen, K., Vaughan, J.E., Eds.; North Holland: Amsterdam, The Netherlands; New York, NY, USA; Oxford, UK, 1984
    • (1984) Handbook of Set-Theoretic Topology
    • Hodel, R.E.1
  • 13
    • 0011674321 scopus 로고
    • Cartesian products and dyadic spaces
    • Engelking, R. Cartesian products and dyadic spaces. Fundam. Math. 1965, 57, 287-304
    • (1965) Fundam. Math , vol.57 , pp. 287-304
    • Engelking, R.1
  • 14
    • 84911591602 scopus 로고
    • Natural covers and r-quotient mappings
    • Karnik, S.M.; Willard, S. Natural covers and r-quotient mappings. Can. Math. Bull. 1982, 25, 456-462
    • (1982) Can. Math. Bull , vol.25 , pp. 456-462
    • Karnik, S.M.1    Willard, S.2
  • 15
    • 50049091740 scopus 로고    scopus 로고
    • Topological groups with dense compactly generated subgroups
    • Fujita, H.; Shakhmatov, D. Topological groups with dense compactly generated subgroups. Appl. Gen. Topol. 2002, 3, 85-89
    • (2002) Appl. Gen. Topol , vol.3 , pp. 85-89
    • Fujita, H.1    Shakhmatov, D.2
  • 16
    • 0001548974 scopus 로고
    • On topological groups close to being Lindelöf
    • Guran, I.I. On topological groups close to being Lindelöf. Sov. Math. Dokl. 1981, 23, 173-175
    • (1981) Sov. Math. Dokl , vol.23 , pp. 173-175
    • Guran, I.I.1
  • 18
    • 0011697893 scopus 로고
    • On the density character of compact topological groups
    • Itzkowitz, G.L. On the density character of compact topological groups. Fundam. Math. 1972, 75, 201-203
    • (1972) Fundam. Math , vol.75 , pp. 201-203
    • Itzkowitz, G.L.1
  • 19
    • 0348102076 scopus 로고
    • Density character in topological groups
    • Comfort, W.W.; Itzkowitz, G.L. Density character in topological groups. Math. Ann. 1977, 226, 223-227
    • (1977) Math. Ann , vol.226 , pp. 223-227
    • Comfort, W.W.1    Itzkowitz, G.L.2
  • 20
    • 84968505551 scopus 로고
    • Characterization of separability for LF-spaces
    • Vidossich, G. Characterization of separability for LF-spaces. Annales de L'institut Fourier 1968, 18, 87-90
    • (1968) Annales de L'institut Fourier , vol.18 , pp. 87-90
    • Vidossich, G.1
  • 21
    • 84966241429 scopus 로고
    • On separability in linear topological spaces
    • Lohman, R.H.; Stiles, W.J. On separability in linear topological spaces. Proc. Am. Math. Soc. 1974, 42, 236-237
    • (1974) Proc. Am. Math. Soc , vol.42 , pp. 236-237
    • Lohman, R.H.1    Stiles, W.J.2
  • 22
    • 84974069726 scopus 로고
    • Varieties of topological groups
    • Morris, S.A. Varieties of topological groups. Bull. Aust. Math. Soc. 1969, 1, 145-160
    • (1969) Bull. Aust. Math. Soc , vol.1 , pp. 145-160
    • Morris, S.A.1
  • 23
    • 84959659642 scopus 로고
    • Varieties of topological groups II
    • Morris, S.A. Varieties of topological groups II. Bull. Aust. Math. Soc. 1970, 2, 1-13
    • (1970) Bull. Aust. Math. Soc , vol.2 , pp. 1-13
    • Morris, S.A.1
  • 24
    • 0011321524 scopus 로고
    • Varieties of topological groups III
    • Morris, S.A. Varieties of topological groups III. Bull. Aust. Math. Soc. 1970, 2, 165-178
    • (1970) Bull. Aust. Math. Soc , vol.2 , pp. 165-178
    • Morris, S.A.1
  • 25
    • 0001115025 scopus 로고
    • Varieties of topological groups a survey
    • Morris, S.A. Varieties of topological groups a survey. Colloq. Math. 1982, 2, 147-165
    • (1982) Colloq. Math , vol.2 , pp. 147-165
    • Morris, S.A.1
  • 29
    • 84981280551 scopus 로고    scopus 로고
    • Pro-Lie groups: A survey with open problems
    • Hofmann, K.H.; Morris, S.A. Pro-Lie groups: A survey with open problems. Axioms 2015, 4, 294-312
    • (2015) Axioms , vol.4 , pp. 294-312
    • Hofmann, K.H.1    Morris, S.A.2
  • 30
    • 85008619321 scopus 로고
    • On the separable topological vector spaces
    • Domański, P. On the separable topological vector spaces. Funct. Approx. Comment. Math. 1984, 14, 117-122
    • (1984) Funct. Approx. Comment. Math , vol.14 , pp. 117-122
    • Domański, P.1
  • 31
    • 34250151493 scopus 로고
    • Nonseparable closed subspaces in separable products of topological vector spaces, and q-minimality
    • Domański, P. Nonseparable closed subspaces in separable products of topological vector spaces, and q-minimality. Arch. Math. 1983, 41, 270-275
    • (1983) Arch. Math , vol.41 , pp. 270-275
    • Domański, P.1
  • 32
    • 33646840276 scopus 로고
    • Varieties of locally convex topological vector spaces
    • Diestel, J.; Morris, S.A.; Saxon, S.A. Varieties of locally convex topological vector spaces. Bull. Am. Math. Soc. 1971, 77, 799-803
    • (1971) Bull. Am. Math. Soc , vol.77 , pp. 799-803
    • Diestel, J.1    Morris, S.A.2    Saxon, S.A.3
  • 34
    • 84858763189 scopus 로고
    • Remarks on varieties of locally convex linear topological spaces
    • Morris, S.A.; Diestel, J. Remarks on varieties of locally convex linear topological spaces. J. Lond. Math. Soc. 1974, 8, 271-278
    • (1974) J. Lond. Math. Soc , vol.8 , pp. 271-278
    • Morris, S.A.1    Diestel, J.2
  • 35
    • 85021404488 scopus 로고    scopus 로고
    • Separable quotients in Cc(X), Cp(X), and their duals
    • Kakol, J.; Saxon, S.A. Separable quotients in Cc(X), Cp(X), and their duals. Proc. Am. Math. Soc. 2017, 145, 3829-3841
    • (2017) Proc. Am. Math. Soc , vol.145 , pp. 3829-3841
    • Kakol, J.1    Saxon, S.A.2
  • 36
    • 84938419851 scopus 로고    scopus 로고
    • Barrelled spaces with(out) separable quotients
    • Kakol, J.; Saxon, S.A.; Todd, A. Barrelled spaces with(out) separable quotients. Bull. Aust. Math. Soc. 2014, 90, 295-303
    • (2014) Bull. Aust. Math. Soc , vol.90 , pp. 295-303
    • Kakol, J.1    Saxon, S.A.2    Todd, A.3
  • 40
    • 77956970899 scopus 로고
    • On a problem of Kurosh, Jonsson groups, and applications
    • Amsterdam, The Netherlands
    • Shelah, S. On a problem of Kurosh, Jonsson groups, and applications. In Word Problems Vol II; Amsterdam, The Netherlands, 1980; pp. 373-394
    • (1980) Word Problems Vol II , pp. 373-394
    • Shelah, S.1
  • 41
    • 15944361951 scopus 로고    scopus 로고
    • Non-discrete topological groups with many discrete subgroups
    • Morris, S.A.; Obraztsov, V.N. Non-discrete topological groups with many discrete subgroups. Topol. Appl. 1998, 84, 105-120
    • (1998) Topol. Appl , vol.84 , pp. 105-120
    • Morris, S.A.1    Obraztsov, V.N.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.