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


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.


Bounded set docile space Mackey first countable inductive limit 

MR(2000) Subject Classification

46A03 46A13 


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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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