Notes on Fréchet spaces

• Main Author: Woo Chorl Hong
• Format: Article
• Language: English
• Published: Hindawi Limited 1999-01-01
• Series: International Journal of Mathematics and Mathematical Sciences
• Subjects: Fréchet; sequential; sequential convergence structures; sequential closure operators; simple expansions; semi-metrizable; symmetrizable; weakly first countable.
• Online Access: http://dx.doi.org/10.1155/S0161171299226592

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.