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International Journal of Mathematics and Mathematical Sciences
Volume 22, Issue 3, Pages 659-665

Notes on Fréchet spaces

Department of Mathematics Education, Pusan National University, Pusan 609-735, Korea

Received 23 July 1999

Copyright © 1999 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


First, we introduce sequential convergence structures and characterize Fréchet spaces and continuous functions in Fréchet spaces using these structures. Second, we give sufficient conditions for the expansion of a topological space by the sequential closure operator to be a Fréchet space and also a sufficient condition for a simple expansion of a topological space to be Fréchet. Finally, we study on a sufficient condition that a sequential space be Fréchet, a weakly first countable space be first countable, and a symmetrizable space be semi-metrizable.