Notes on Fréchet spaces

Woo Chorl Hong

International Journal of Mathematics and Mathematical Sciences, 1999, vol. 22, 1-7

Abstract:

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.

Date: 1999
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:147539

DOI: 10.1155/S0161171299226592

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