ON TOPOLOGICAL CLASSIFICATION OF NON-ARCHIMEDEAN FréCHET SPACES


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Abstract

We prove that any infinite-dimensional non-archimedean Fréchet space E is homeomorphic to D where D is a discrete space with card(D) = dens(E). It follows that infinite-dimensional non-archimedean Fréchet spaces E and F are homeomorphic if and only if dens(E) = dens(F). In particular, any infinite-dimensional non-archimedean Fréchet space of countable type over a field 𝕂 is homeomorphic to the non-archimedean Fréchet space 𝕂.

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