2024/04/21 by Sebastián Barría, Barría, Sebastián
Mathematics · #54A20 #54B10 #54B20 #54D30 #54E35 #54F05 #FOS: Mathematics #General Topology (math.GN) #History and Theory of Mathematics
paper · pdf · doi:10.48550/arxiv.2404.13741
openalex publication_date 2024/04/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let \mathbbA and \mathbbS denote the double arrow of Alexandroff and the Sorgenfrey line, respectively. We show that for any n≥ 1, the space of all unions of at most n closed intervals of \mathbbA is not homogeneous. We also prove that the spaces of non-trivial convergent sequences of \mathbbA and \mathbbS are homogeneous. This partially solves an open question of A. Arhangel'skiǐ. In contrast, we show that the space of closed intervals of \mathbbS is homogeneous.