Completeness of certain function spaces

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Abstract

We give an example of a complete locally convex m-topology on the algebra of infinite differentiable functions on [0, 1] which is strictly coarser than the natural Frechet-topology but finer than the topology of pointwise convergence. A similar construction works on the algebra of continuous functions on [0, 1]. Using this examples we can separate different notions of diffotopy and homotopy.
Original languageEnglish
Pages (from-to)509-512
Number of pages4
JournalBulletin of the Belgian Mathematical Society
Volume14
Issue number3
Publication statusPublished - Jul 2007

ASJC Scopus subject areas

  • Mathematics(all)

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