Abstract
Let A and S 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 A is not homogeneous. We also prove that the spaces of non-trivial convergent sequences of A and S are homogeneous. This partially solves an open question of A. Arhangel'skiǐ [1]. In contrast, we show that the space of closed intervals of S is homogeneous.
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