Descriptive Topology in non-Archimedean Function Spaces Cp(X, K). Part I
| dc.contributor.author | Śliwa, Wiesław | |
| dc.contributor.author | Kąkol, Jerzy | |
| dc.date.accessioned | 2013-02-06T08:24:11Z | |
| dc.date.available | 2013-02-06T08:24:11Z | |
| dc.date.issued | 2012 | |
| dc.description.abstract | Let $K$ be a non-archimedean field and let $X$ be an ultraregular space. We study the non-archimedean locally convex space $C_p(X;K)$ of all $K$-valued continuous functions on $X$ endowed with the pointwise topology. We show that $K$ is spherically complete if and only if every polar metrizable locally convex space $E$ over $K$ is weakly angelic. This extends a result of Kiyosawa - Schikhof for polar Banach spaces. For any compact ultraregular space $X$ we prove that $C_p(X;K)$ is Frechet-Urysohn if and only if $X$ is scattered (a non-archimedean variant of Gerlits - Pytkeev's result). If $K$ is locally compact we show the following: (1) For any ultraregular space $X$ the space $C_p(X;K)$ is K-analytic if and only if it has a compact resolution (a non-archimedean variant of Tkachuk's theorem); (2) For any ultrametrizable space $X$ the space $C_p(X;K)$ is analytic if and only if $X$ is $\sigma$-compact (a non-archimedean variant of Christensen's theorem). | pl_PL |
| dc.description.sponsorship | The National Centre of Science, Poland (grant no. N N201 605340) | pl_PL |
| dc.identifier.citation | Bull. London Math. Soc., 44(2012), 899-912 | pl_PL |
| dc.identifier.uri | http://hdl.handle.net/10593/4327 | |
| dc.language.iso | en | pl_PL |
| dc.title | Descriptive Topology in non-Archimedean Function Spaces Cp(X, K). Part I | pl_PL |