Geodesic
A non-archimedean Dugundji extension theorem
Czechoslovak Mathematical Journal, Tome 63 (2013) no. 1, pp. 157-164 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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We prove a non-archimedean Dugundji extension theorem for the spaces $C^{\ast }(X,\mathbb {K})$ of continuous bounded functions on an ultranormal space $X$ with values in a non-archimedean non-trivially valued complete field $\mathbb {K}$. Assuming that $\mathbb {K}$ is discretely valued and $Y$ is a closed subspace of $X$ we show that there exists an isometric linear extender $T\colon C^{\ast }(Y,\mathbb {K})\rightarrow C^{\ast }(X,\mathbb {K})$ if $X$ is collectionwise normal or $Y$ is Lindelöf or $\mathbb {K}$ is separable. We provide also a self contained proof of the known fact that any metrizable compact subspace $Y$ of an ultraregular space $X$ is a retract of $X$.
We prove a non-archimedean Dugundji extension theorem for the spaces $C^{\ast }(X,\mathbb {K})$ of continuous bounded functions on an ultranormal space $X$ with values in a non-archimedean non-trivially valued complete field $\mathbb {K}$. Assuming that $\mathbb {K}$ is discretely valued and $Y$ is a closed subspace of $X$ we show that there exists an isometric linear extender $T\colon C^{\ast }(Y,\mathbb {K})\rightarrow C^{\ast }(X,\mathbb {K})$ if $X$ is collectionwise normal or $Y$ is Lindelöf or $\mathbb {K}$ is separable. We provide also a self contained proof of the known fact that any metrizable compact subspace $Y$ of an ultraregular space $X$ is a retract of $X$.
DOI : 10.1007/s10587-013-0010-8
Classification : 46S10, 54C35
Keywords: Dugundji extension theorem; non-archimedean space; space of continuous functions; 0-dimensional space 
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     title = {A non-archimedean {Dugundji} extension theorem},
     journal = {Czechoslovak Mathematical Journal},
     pages = {157--164},
     year = {2013},
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     number = {1},
     doi = {10.1007/s10587-013-0010-8},
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     zbl = {1274.46131},
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Kąkol, Jerzy; Kubzdela, Albert; Śliwa, Wiesław. A non-archimedean Dugundji extension theorem. Czechoslovak Mathematical Journal, Tome 63 (2013) no. 1, pp. 157-164. doi: 10.1007/s10587-013-0010-8

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