Abstract
Each ordinal α equipped with the upper topology is a T 0-space. It is well known that for α=2 the reflective hull of α in Top0 is the subcategory of sober spaces. Here, we define α-sober space for each α≥2 in such a way that the reflective hull of α in Top0 is the subcategory of α-sober spaces. Moreover, we obtain an order-preserving bijective correspondence between a proper class of ordinals and the corresponding (epi)reflective hulls. Our main tool is the concept of orthogonal closure operator, first introduced in [12].
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The author acknowledges financial support from Instituto Politécnico de Viseu and from Centro de Matemática da Universidade de Coimbra.
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Sousa, L. α-Sober spaces via the orthogonal closure operator. Appl Categor Struct 4, 87–95 (1996). https://doi.org/10.1007/BF00124117
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DOI: https://doi.org/10.1007/BF00124117