Abstract
We generalise some results of R. E. Stong concerning finite spaces to wider subclasses of Alexandroff spaces. In particular, we characterize pairs of spaces X,Y such that the compact-open topology on C(X,Y) is Alexandroff, give a homotopy type classification of a class of infinite Alexandroff spaces and prove some results concerning cores of locally finite spaces. We also discuss a mistake found in an article of F.G. Arenas. Since the category of T 0 Alexandroff spaces is equivalent to the category of posets, our results may lead to a deeper understanding of the notion of a core of an infinite poset.
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Kukieła, M.J. On Homotopy Types of Alexandroff Spaces. Order 27, 9–21 (2010). https://doi.org/10.1007/s11083-009-9134-8
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DOI: https://doi.org/10.1007/s11083-009-9134-8