2020/03/29 by Gutev, Valentin
#54B20 #54C65 #54D05 #54E35 #54F05 #54F50 #FOS: Mathematics #General Topology (math.GN)
paper · doi:10.48550/arxiv.2003.13134
Each continuous weak selection for a space X defines a coarser topology on X, called a selection topology. Spaces whose topology is determined by a collection of such selection topologies are called continuous weak selection spaces. For such spaces, Garc'ıa-Ferreira, Miyazaki, Nogura and Tomita considered the minimal number cws(X) of selection topologies which generate the original topology of X, and called it the cws-number of X. In this paper, we show that cws(X)≤ 2 for every semi-orderable space X, and that cws(X)=2 precisely when such a space X has two components and is not orderable. Complementary to this result, we also show that cws(X)=1 for each suborderable metrizable space X which has at least 3 components.