A non-metrizable compact linearly ordered topological space, every subspace of which has a <IMG ALIGN=BOTTOM HEIGHT=9 WIDTH=10>-minimal base期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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A non-metrizable compact linearly ordered topological space, every subspace of which has a -minimal base

Authors:	Wei-Xue Shi

Institution:	Department of Mathematics, Changchun Teachers College, Changchun 130032, China

Abstract:	A collection $\begin{math}\mathcal{D}\end{math}$ of subsets of a space is minimal if each element of $\begin{math}\mathcal{D}\end{math}$ contains a point which is not contained in any other element of $\begin{math}\mathcal{D}\end{math}$ . A base of a topological space is $\begin{math}\sigma\end{math}$ -minimal if it can be written as a union of countably many minimal collections. We will construct a compact linearly ordered space $\begin{math}X\end{math}$ satisfying that $\begin{math}X\end{math}$ is not metrizable and every subspace of $\begin{math}X\end{math}$ has a $\begin{math}\sigma\end{math}$ -minimal base for its relative topology. This answers a problem of Bennett and Lutzer in the negative.

Keywords:	$\sigma$-minimal base metrizable linearly ordered topological space special Aronszajn tree quasi-developable

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