On perfect images of ordinals

In the first section of this paper, the ordinal space [1, ω] is characterized. Then its quotients are completely described in easy terms. In the second section, the ideas of a well-ordered sum of an arbitrary collection of T₂spaces and a Chandelier space are introduced. The Chandelier spaces are obtained by taking compact ordinals and forming their interweaves and well ordered sums and one-point compactification of such spaces. Finally it is proved that the Hausdorff quotients of compact ordinals are precisely the Chandelier spaces. A problem of M. Huek on quotients of [1, ω] is thus solved.