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Volumn 24, Issue 3, 2017, Pages

Reinventing weak barrelledness

Author keywords

Countable enlargements; Dual locally complete; Measurable cardinals; Optimal results; Primitive; barrelled

Indexed keywords


EID: 85020135439     PISSN: 09446532     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (10)

References (71)
  • 1
    • 0000445369 scopus 로고
    • Über nicht-vollständige Montelräume
    • I. Amemiya and Y. Kōmura, Über nicht-vollständige Montelräume, Math. Ann. 177(1968), 273-277.
    • (1968) Math. Ann. , vol.177 , pp. 273-277
    • Amemiya, I.1    Komura, Y.2
  • 4
    • 0042740881 scopus 로고
    • Varieties of linear topological vector spaces
    • J. Diestel, S. Morris and S. Saxon, Varieties of linear topological vector spaces, Trans. Amer. Math. Soc. 172(1972), 207-230.
    • (1972) Trans. Amer. Math. Soc. , vol.172 , pp. 207-230
    • Diestel, J.1    Morris, S.2    Saxon, S.3
  • 7
    • 33646969211 scopus 로고
    • Una propiedad de M. Valdivia, espacios de tipo (L) y condiciones débiles de tonelación
    • J. C. Ferrando and M. López Pellicer, Una propiedad de M. Valdivia, espacios de tipo (L) y condiciones débiles de tonelación, Rev. Re. Ac. Ci. Ex. Fís. y Nat. 83(1991), 25-34.
    • (1991) Rev. Re. Ac. Ci. Ex. Fís. Y Nat. , vol.83 , pp. 25-34
    • Ferrando, J.C.1    López Pellicer, M.2
  • 11
    • 33746739366 scopus 로고
    • A generalized form of inductive-limit topology for vector spaces
    • D. J. H. Garling, A generalized form of inductive-limit topology for vector spaces, Lond. Math. Soc. (3) 14(1964), 1-28.
    • (1964) Lond. Math. Soc. , vol.3 , Issue.14 , pp. 1-28
    • Garling, D.J.H.1
  • 12
    • 0008978614 scopus 로고
    • Two new classes of locally convex spaces
    • T. Husain, Two new classes of locally convex spaces, Math. Ann. 166(1966), 289-299.
    • (1966) Math. Ann. , vol.166 , pp. 289-299
    • Husain, T.1
  • 14
    • 0003203337 scopus 로고
    • Weak sequential convergence in the dual of a Banach space does not imply norm convergence
    • B. Josefson, Weak sequential convergence in the dual of a Banach space does not imply norm convergence, Archiv für Mathematik 13(1975), 79-89.
    • (1975) Archiv für Mathematik , vol.13 , pp. 79-89
    • Josefson, B.1
  • 15
    • 84859485208 scopus 로고    scopus 로고
    • Descriptive Topology in Selected Topics of Functional Analysis
    • Springer
    • Jerzy Kąkol, Wiesław Kubiś and M. López-Pellicer, Descriptive Topology in Selected Topics of Functional Analysis, DEVM 24, Springer, 2011.
    • (2011) DEVM , vol.24
    • Kakol, J.1    Kubiś, W.2    López-Pellicer, M.3
  • 16
  • 17
    • 0036961820 scopus 로고    scopus 로고
    • The Fréchet-Urysohn view of weak and s-barrelledness
    • special volume in honor of De Kimpe and Van hamme
    • Jerzy Kąkol and Stephen A. Saxon, The Fréchet-Urysohn view of weak and s-barrelledness, Bull. Belgian Math. Soc., special volume in honor of De Kimpe and Van hamme (2002), 101-108.
    • (2002) Bull. Belgian Math. Soc. , pp. 101-108
    • Kakol, J.1    Saxon, S.A.2
  • 18
    • 4444223403 scopus 로고    scopus 로고
    • Weak barrelledness for C (X) spaces
    • Jerzy Kąkol, Stephen A. Saxon and Aaron R. Todd, Weak barrelledness for C (X) spaces, J. Math. Anal. Appl. 297(2004), 495-505.
    • (2004) J. Math. Anal. Appl. , vol.297 , pp. 495-505
    • Kakol, J.1    Saxon, S.A.2    Todd, A.R.3
  • 19
    • 84938419851 scopus 로고    scopus 로고
    • Barrelled spaces with(out) separable quotients
    • Jerzy Kąkol, Stephen A. Saxon and Aaron R. Todd, Barrelled spaces with(out) separable quotients, Bull. Austral. Math. Soc. 90(2014), 295-303. doi: 10.1017/S0004972714000422
    • (2014) Bull. Austral. Math. Soc. , vol.90 , pp. 295-303
    • Kakol, J.1    Saxon, S.A.2    Todd, A.R.3
  • 20
    • 84976193393 scopus 로고
    • Some forms of the closed graph theorem
    • N. J. Kalton, Some forms of the closed graph theorem, Proc. Camb. Phil. Soc. 70(1971), 401-408.
    • (1971) Proc. Camb. Phil. Soc. , vol.70 , pp. 401-408
    • Kalton, N.J.1
  • 22
    • 0004279221 scopus 로고
    • North-Holland, Amsterdam
    • K. Kunen, Set theory, North-Holland, Amsterdam, 1980.
    • (1980) Set Theory
    • Kunen, K.1
  • 23
    • 0003225456 scopus 로고
    • Barrelledness, Baire-like-, and (LF)-spaces
    • Longman
    • M. Kunzinger, Barrelledness, Baire-like-, and (LF)-spaces, Pitman RNMS 298, Longman, 1993.
    • (1993) Pitman RNMS , vol.298
    • Kunzinger, M.1
  • 24
    • 84968512214 scopus 로고
    • A note on the inheritance of properties of locally convex spaces by subspaces of countable codimension
    • M. Levin and S. Saxon, A note on the inheritance of properties of locally convex spaces by subspaces of countable codimension, Proc. Amer. Math. Soc. 29(1971), 97-102.
    • (1971) Proc. Amer. Math. Soc. , vol.29 , pp. 97-102
    • Levin, M.1    Saxon, S.2
  • 25
    • 51249189988 scopus 로고
    • w∗ sequential convergence
    • A. Nissenzweig, w∗ sequential convergence, Israel J. Math. 22(1975), 266-272.
    • (1975) Israel J. Math. , vol.22 , pp. 266-272
    • Nissenzweig, A.1
  • 26
    • 0003236344 scopus 로고
    • Barrelled Locally Convex Spaces
    • North Holland
    • P. Pérez Carreras and J. Bonet, Barrelled Locally Convex Spaces, Math. Studies 131, North Holland, 1987.
    • (1987) Math. Studies , vol.131
    • Pérez Carreras, P.1    Bonet, J.2
  • 27
  • 28
    • 23044528308 scopus 로고    scopus 로고
    • Local completeness and dual local quasicompleteness
    • Jinghui Qiu, Local completeness and dual local quasicompleteness, Proc. Amer. Math. Soc. 129(2000), 1419-1425.
    • (2000) Proc. Amer. Math. Soc. , vol.129 , pp. 1419-1425
    • Qiu, J.1
  • 29
    • 0011635556 scopus 로고
    • On the Cartesian Product of Two Compact Spaces
    • J. Novák, On the Cartesian Product of Two Compact Spaces, Fund. Math. 40(1953), 106-112.
    • (1953) Fund. Math. , vol.40 , pp. 106-112
    • Novák, J.1
  • 30
    • 84974252524 scopus 로고
    • On properly separable quotients of strict (LF)-spaces
    • W. J. Robertson, On properly separable quotients of strict (LF)-spaces, J. Austral. Math. Soc. 47(1989), 307-312.
    • (1989) J. Austral. Math. Soc. , vol.47 , pp. 307-312
    • Robertson, W.J.1
  • 33
    • 0039252354 scopus 로고
    • On the finest locally convex topology agreeing with a given topology on a sequence of absolutely convex sets
    • W. Roelcke, On the finest locally convex topology agreeing with a given topology on a sequence of absolutely convex sets, Math. Ann. 198(1974), 57-80.
    • (1974) Math. Ann. , vol.198 , pp. 57-80
    • Roelcke, W.1
  • 34
    • 0012672525 scopus 로고
    • A Grothendieck representation for the completion of cones of continuous semi-norms
    • W. Ruess, A Grothendieck representation for the completion of cones of continuous semi-norms, Math. Ann. 208(1974), 71-90.
    • (1974) Math. Ann. , vol.208 , pp. 71-90
    • Ruess, W.1
  • 35
    • 84972492739 scopus 로고
    • Generalized inductive limit topologies and barrelledness properties
    • W. Ruess, Generalized inductive limit topologies and barrelledness properties, Pac. J. Math. 63, no. 2(1976), 499-516.
    • (1976) Pac. J. Math. , vol.63 , Issue.2 , pp. 499-516
    • Ruess, W.1
  • 36
    • 33646984845 scopus 로고
    • Closed graph theorems for generalized inductive limit topologies
    • W. Ruess, Closed graph theorems for generalized inductive limit topologies, Math. Proc. Camb. Phil. Soc. 82(1977), 67-83.
    • (1977) Math. Proc. Camb. Phil. Soc. , vol.82 , pp. 67-83
    • Ruess, W.1
  • 37
    • 84972496126 scopus 로고
    • [Weakly] Compact operators and DF spaces
    • W. Ruess, [Weakly] Compact operators and DF spaces, Pac. J. Math. 98(1982), 419-441.
    • (1982) Pac. J. Math. , vol.98 , pp. 419-441
    • Ruess, W.1
  • 39
    • 0003090307 scopus 로고
    • Nuclear and product spaces, Baire-like spaces, and the strongest locally convex topology
    • S. A. Saxon, Nuclear and product spaces, Baire-like spaces, and the strongest locally convex topology, Math. Ann. 197(1972), 87-106.
    • (1972) Math. Ann. , vol.197 , pp. 87-106
    • Saxon, S.A.1
  • 40
    • 84966230050 scopus 로고
    • Two characterizations of linear Baire spaces
    • S. A. Saxon, Two characterizations of linear Baire spaces, Proc. Amer. Math. Soc. 45(1974), 204-208.
    • (1974) Proc. Amer. Math. Soc. , vol.45 , pp. 204-208
    • Saxon, S.A.1
  • 41
    • 18044397889 scopus 로고
    • The codensity character of topological vector spaces
    • A. Lau and I. Tweddle, Editors Pitman RNMS Longman
    • S. A. Saxon, The codensity character of topological vector spaces, in Topological vector spaces, algebras and related areas, (A. Lau and I. Tweddle, Editors) Pitman RNMS 316, Longman, 1994, pp. 24-36.
    • (1994) Topological Vector Spaces, Algebras and Related Areas , vol.316 , pp. 24-36
    • Saxon, S.A.1
  • 42
    • 0012598599 scopus 로고    scopus 로고
    • Metrizable barrelled countable enlargements
    • S. A. Saxon, Metrizable barrelled countable enlargements, Bull. Lond. Math. Soc. 31(1999), 711-718.
    • (1999) Bull. Lond. Math. Soc. , vol.31 , pp. 711-718
    • Saxon, S.A.1
  • 43
    • 84906696490 scopus 로고    scopus 로고
    • Mackey hyperplanes/enlargements for Tweddle's space
    • S. A. Saxon, Mackey hyperplanes/enlargements for Tweddle's space, RACSAM 108(2014), pp. 1035-1054. doi: 10.1007/s13398-013-0159-x
    • (2014) RACSAM , vol.108 , pp. 1035-1054
    • Saxon, S.A.1
  • 44
    • 84927798417 scopus 로고    scopus 로고
    • Weak barrelledness vs. P-spaces
    • J. C. Ferrando and M. López-Pellicer, Editors) Springer PROMS
    • S. A. Saxon, Weak barrelledness vs. P-spaces, in Descriptive Topology and Functional Analysis, (J. C. Ferrando and M. López-Pellicer, Editors) Springer PROMS 80, 2014, pp. 27-32. doi: 10.1007/978-3-319-05224-3-2
    • (2014) Descriptive Topology and Functional Analysis , vol.80 , pp. 27-32
    • Saxon, S.A.1
  • 45
    • 84943364946 scopus 로고    scopus 로고
    • (LF)-spaces with more-than-separable quotients
    • to appear
    • S. A. Saxon, (LF)-spaces with more-than-separable quotients, J. Math. Anal. Appl., to appear. doi: 10.1016/j.jmaa.2015.09.005
    • J. Math. Anal. Appl.
    • Saxon, S.A.1
  • 46
    • 0002095433 scopus 로고
    • Every countable-codimensional subspace of a barrelled space is barrelled
    • S. Saxon and M. Levin, Every countable-codimensional subspace of a barrelled space is barrelled, Proc. Amer. Math. Soc. 29(1971), 91-96.
    • (1971) Proc. Amer. Math. Soc. , vol.29 , pp. 91-96
    • Saxon, S.1    Levin, M.2
  • 47
    • 0000878326 scopus 로고
    • (LF)-spaces, quasi-Baire spaces and the strongest locally convex topology
    • S. A. Saxon and P. P. Narayanaswami, (LF)-spaces, quasi-Baire spaces and the strongest locally convex topology, Math. Ann. 274(1986), 627-641.
    • (1986) Math. Ann. , vol.274 , pp. 627-641
    • Saxon, S.A.1    Narayanaswami, P.P.2
  • 48
    • 0011268979 scopus 로고
    • Metrizable [normable] (LF)-spaces and two classical problems in Fréchet [Banach] spaces
    • S. A. Saxon and P. P. Narayanaswami, Metrizable [normable] (LF)-spaces and two classical problems in Fréchet [Banach] spaces, Studia Math. 93(1989), 1-16.
    • (1989) Studia Math. , vol.93 , pp. 1-16
    • Saxon, S.A.1    Narayanaswami, P.P.2
  • 49
    • 0000353012 scopus 로고
    • Dense barrelled subspaces of uncountable codimension
    • S. A. Saxon and W. J. Robertson, Dense barrelled subspaces of uncountable codimension, Proc. Amer. Math. Soc. 107(1989), 1021-1029.
    • (1989) Proc. Amer. Math. Soc. , vol.107 , pp. 1021-1029
    • Saxon, S.A.1    Robertson, W.J.2
  • 50
    • 0030295727 scopus 로고    scopus 로고
    • Barrelled countable enlargements and the dominating cardinal
    • S. A. Saxon and L. M. Sánchez Ruiz, Barrelled countable enlargements and the dominating cardinal, J. Math. Anal. Appl. 203(1996), 677-685.
    • (1996) J. Math. Anal. Appl. , vol.203 , pp. 677-685
    • Saxon, S.A.1    Sánchez Ruiz, L.M.2
  • 57
    • 84974307782 scopus 로고
    • The fit and flat components of barrelled spaces
    • Stephen A. Saxon and Ian Tweddle, The fit and flat components of barrelled spaces, Bull. Austral. Math. Soc. 51(1995), 521-528.
    • (1995) Bull. Austral. Math. Soc. , vol.51 , pp. 521-528
    • Saxon, S.A.1    Tweddle, I.2
  • 58
    • 0001047025 scopus 로고
    • The equivalence of some Banach space problems
    • S. Saxon and A. Wilansky, The equivalence of some Banach space problems, Colloq. Math. 37(1977), 217-266.
    • (1977) Colloq. Math. , vol.37 , pp. 217-266
    • Saxon, S.1    Wilansky, A.2
  • 61
    • 33646973287 scopus 로고
    • Countable enlargements and weak barrelledness conditions
    • (A. Lau and I. Tweddle, Editors) Pitman RNMS Longman
    • I. Tweddle and F. X. Catalán, Countable enlargements and weak barrelledness conditions, in Topological vector spaces, algebras and related areas, (A. Lau and I. Tweddle, Editors) Pitman RNMS 316, Longman, 1994, pp. 56-65.
    • (1994) Topological Vector Spaces, Algebras and Related Areas , vol.316 , pp. 56-65
    • Tweddle, I.1    Catalán, F.X.2
  • 62
  • 63
    • 84971160015 scopus 로고
    • On the stability of barrelled topologies II
    • I. Tweddle and F. E. Yeomans, On the stability of barrelled topologies II, Bull. Austral. Math. Soc. 22(1980), 99-112.
    • (1980) Bull. Austral. Math. Soc. , vol.22 , pp. 99-112
    • Tweddle, I.1    Yeomans, F.E.2
  • 64
    • 0002171533 scopus 로고
    • Absolutely convex sets in barrelled spaces
    • M. Valdivia, Absolutely convex sets in barrelled spaces, Ann. Inst. Fourier 21(1971), 3-13.
    • (1971) Ann. Inst. Fourier , vol.21 , pp. 3-13
    • Valdivia, M.1
  • 65
    • 84931154962 scopus 로고
    • On Mackey spaces
    • M. Valdivia, On Mackey spaces, Duke Math J. 41(1974), 57-66.
    • (1974) Duke Math J , vol.41 , pp. 57-66
    • Valdivia, M.1
  • 66
    • 0011008425 scopus 로고
    • Mackey convergence and the closed graph theorem
    • M. Valdivia, Mackey convergence and the closed graph theorem, Arch. Math. 25(1974), 649-656.
    • (1974) Arch. Math. , vol.25 , pp. 649-656
    • Valdivia, M.1
  • 67
    • 33646976977 scopus 로고
    • On quasi-completeness and sequential completeness in locally convex spaces
    • M. Valdivia, On quasi-completeness and sequential completeness in locally convex spaces, J. Reine Angew. Math. 276(1975), 190-199.
    • (1975) J. Reine Angew. Math. , vol.276 , pp. 190-199
    • Valdivia, M.1
  • 68
    • 0003234874 scopus 로고
    • Topics in Locally Convex Spaces
    • North Holland
    • M. Valdivia, Topics in Locally Convex Spaces, Math. Studies 67, North Holland, 1982.
    • (1982) Math. Studies , vol.67
    • Valdivia, M.1
  • 69
    • 84971120922 scopus 로고
    • Sequential convergence in locally convex spaces
    • J. H. Webb, Sequential convergence in locally convex spaces, Proc. Camb. Phil. Soc. 64(1968), 341-364.
    • (1968) Proc. Camb. Phil. Soc. , vol.64 , pp. 341-364
    • Webb, J.H.1
  • 70
    • 0011638089 scopus 로고
    • Topics in Functional Analysis
    • Springer-Verlag
    • A. Wilansky, Topics in Functional Analysis, LNM 45, Springer-Verlag, 1967
    • (1967) LNM , vol.45
    • Wilansky, A.1


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