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.
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Bosch Giral, C., Gilsdorf, T.E. & Gómez-Wulschner, C. Mackey first countability and docile locally convex spaces. Acta. Math. Sin.-English Ser. 27, 737–740 (2011). https://doi.org/10.1007/s10114-011-8540-1
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DOI: https://doi.org/10.1007/s10114-011-8540-1