On topological classification of non-archimedean Fréchet spaces

Wiesƚaw Śliwa

Displaying similar documents to “On topological classification of non-archimedean Fréchet spaces”

A non-archimedean Dugundji extension theorem

Jerzy Kąkol, Albert Kubzdela, Wiesƚaw Śliwa (2013)

Czechoslovak Mathematical Journal

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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 $Y$ ...

An extension of a theorem of Rosenthal on operators acting from $l_{\infty} (Γ)$

L. Drenowski (1976)

Studia Mathematica

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A two well Liouville theorem

Andrew Lorent (2005)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper we analyse the structure of approximate solutions to the compatible two well problem with the constraint that the surface energy of the solution is less than some fixed constant. We prove a quantitative estimate that can be seen as a two well analogue of the Liouville theorem of Friesecke James Müller. Let $H = (\begin{matrix} σ & 0 \\ 0 & σ^{- 1} \end{matrix})$ for $σ > 0$ . Let $0 < ζ_{1} < 1 < ζ_{2} < \infty$ . Let $K : = S O (2) \cup S O (2) H$ . Let $u \in W^{2, 1} (Q_{1} (0))$ be a $C^{1}$ invertible bilipschitz function with $Lip (u) < ζ_{2}$ , $Lip (u^{- 1}) < ζ_{1}^{- 1}$ . There exists positive constants $𝔠_{1} < 1$ and $𝔠_{2} > 1$ depending only on $σ$ , $ζ_{1}$ , $ζ_{2}$ such that if $ϵ \in (0, 𝔠_{1})$ and $u$ ...

Properties of one-point completions of a noncompact metrizable space

Melvin Henriksen, Ludvík Janoš, Grant R. Woods (2005)

Commentationes Mathematicae Universitatis Carolinae

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If a metrizable space $X$ is dense in a metrizable space $Y$ , then $Y$ is called a of $X$ . If $T_{1}$ and $T_{2}$ are metric extensions of $X$ and there is a continuous map of $T_{2}$ into $T_{1}$ keeping $X$ pointwise fixed, we write $T_{1} \leq T_{2}$ . If $X$ is noncompact and metrizable, then $(ℳ (X), \leq)$ denotes the set of metric extensions of $X$ , where $T_{1}$ and $T_{2}$ are identified if $T_{1} \leq T_{2}$ and $T_{2} \leq T_{1}$ , i.e., if there is a homeomorphism of $T_{1}$ onto $T_{2}$ keeping $X$ pointwise fixed. $(ℳ (X), \leq)$ is a large complicated poset studied extensively by V. Bel’nov [, Trans. Moscow Math....

Thickness of a family of sets and uniform measures

Antonín Lešanovský (1988)

Časopis pro pěstování matematiky

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Displaying similar documents to “On topological classification of non-archimedean Fréchet spaces”

A non-archimedean Dugundji extension theorem

An extension of a theorem of Rosenthal on operators acting from l ∞ ( Γ )

A two well Liouville theorem

Properties of one-point completions of a noncompact metrizable space

Thickness of a family of sets and uniform measures

An extension of a theorem of Rosenthal on operators acting from $l_{\infty} (Γ)$