Acta Mathematica Sinica, English Series

, Volume 27, Issue 4, pp 737–740 | Cite as

Mackey first countability and docile locally convex spaces

  • Carlos Bosch Giral
  • Thomas E. Gilsdorf
  • Claudia Gómez-Wulschner
Article
  • 37 Downloads

Abstract

We define a generalization of Mackey first countability and prove that it is equivalent to being docile. A consequence of the main result is to give a partial affirmative answer to an old question of Mackey regarding arbitrary quotients of Mackey first countable spaces. Some applications of the main result to spaces such as inductive limits are also given.

Keywords

Bounded set docile space Mackey first countable inductive limit 

MR(2000) Subject Classification

46A03 46A13 

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References

  1. [1]
    Mackey, G. W.: On infinite-dimensional linear spaces. Trans. Amer. Math. Soc., 66(57), 155–207 (1945)MathSciNetGoogle Scholar
  2. [2]
    Kakol, J., Saxon, S. A.: Montel (DF)-spaces, sequential (LM)-spaces and the strongest locally convex topology. J. London Math. Soc., 66, 388–406 (2002)MathSciNetMATHCrossRefGoogle Scholar
  3. [3]
    Kakol, J., Saxon, S. A., Todd, A. R.: Pseudocompact spaces X and df-spaces C c (X). Proc. Amer. Math. Soc., 132(6), 1703–1712 (2004)MathSciNetMATHCrossRefGoogle Scholar
  4. [4]
    Kummet, C.: Bounded Sets in Locally Convex Spaces, Master’s Thesis, University of North Dakota, 2005Google Scholar
  5. [5]
    Kakol, J., Saxon, S. A., Todd, A. R.: Docile Locally Convex Spaces, Contemp. Math., Vol. 341, Amer. Math. Soc., Providence, RI, 2004, 73–77Google Scholar
  6. [6]
    Pérez Carreras, P., Bonet, J.: Barrelled Locally Convex Spaces, North Holland Math. Studies, Vol. 131, 1987Google Scholar
  7. [7]
    Qiu, J. H.: Characterizations of weakly sequentially retractive (LM)-spaces. Acta Mathematica Sinica, Chinese Series, 49(6), 1231–1238 (2006)MathSciNetMATHGoogle Scholar
  8. [8]
    Horváth, J.: Topological Vector Spaces and Distributions, Vol. 1, Academic Press, New York, 1966Google Scholar

Copyright information

© Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Carlos Bosch Giral
    • 1
  • Thomas E. Gilsdorf
    • 2
  • Claudia Gómez-Wulschner
    • 1
  1. 1.Departamento de MatemáticasITAMMéxico, DFMexico
  2. 2.Department of MathematicsUniversity of North DakotaGrand ForksUSA

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