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Notes on Fréchet spaces

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  • Woo Chorl Hong

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.

Suggested Citation

  • Woo Chorl Hong, 1999. "Notes on Fréchet spaces," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 22, pages 1-7, January.
    • Handle: RePEc:hin:jijmms:147539
    DOI: 10.1155/S0161171299226592
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