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Currently displaying 1 – 3 of 3

Order by Relevance | Title | Year of publication

On topological classification of non-archimedean Fréchet spaces

Wiesƚaw Śliwa — 2004

Czechoslovak Mathematical Journal

We prove that any infinite-dimensional non-archimedean Fréchet space $E$ is homeomorphic to $D^{ℕ}$ where $D$ is a discrete space with $c a r d (D) = d e n s (E)$ . It follows that infinite-dimensional non-archimedean Fréchet spaces $E$ and $F$ are homeomorphic if and only if $d e n s (E) = d e n s (F)$ . In particular, any infinite-dimensional non-archimedean Fréchet space of countable type over a field $𝕂$ is homeomorphic to the non-archimedean Fréchet space $𝕂^{ℕ}$ .

When $(E, σ (E, E^{'}))$ is a $D F$ -space?

Dorota Krassowska; Wiesƚaw Śliwa — 1992

Commentationes Mathematicae Universitatis Carolinae

Let $(E, t)$ be a Hausdorff locally convex space. Either $(E, σ (E, E^{'}))$ or $(E^{'}, σ (E^{'}, E))$ is a $D F$ -space iff $E$ is of finite dimension (THEOREM). This is the most general solution of the problem studied by Iyahen [2] and Radenovič [3].

A non-archimedean Dugundji extension theorem

Jerzy Kąkol; Albert Kubzdela; Wiesƚaw Śliwa — 2013

Czechoslovak Mathematical Journal

We prove a non-archimedean Dugundji extension theorem for the spaces $C^{*} (X, 𝕂)$ of continuous bounded functions on an ultranormal space $X$ with values in a non-archimedean non-trivially valued complete field $𝕂$ . Assuming that $𝕂$ is discretely valued and $Y$ is a closed subspace of $X$ we show that there exists an isometric linear extender $T : C^{*} (Y, 𝕂) \to C^{*} (X, 𝕂)$ if $X$ is collectionwise normal or $Y$ is Lindelöf or $𝕂$ is separable. We provide also a self contained proof of the known fact that any metrizable compact subspace $Y$ of an ultraregular...

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