Mackey first countability and docile locally convex spaces

Carlos Bosch Giral, Thomas E. Gilsdorf, Claudia Gómez-Wulschner

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)737-740
Number of pages4
JournalActa Mathematica Sinica, English Series
Issue number4
StatePublished - Apr 2011


  • Bounded set
  • Mackey first countable
  • docile space
  • inductive limit


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