α-Sober Spaces via the Orthogonal Closure Operator

Lurdes Sousa
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Lurdes Sousa: Instituto Politécnico de Viseu, Campus Politécnico, Repeses, Escola Superior de Tecnologia

A chapter in Categorical Topology, 1996, pp 87-95 from Springer

Abstract: 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 T op 0 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 T op 0 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].

Keywords: Orthogonal closure operator; strongly closed object; (epi)reflective hull; α-sober space; 18A40; 18B30; 18B35; 54B30; 54F65; 04A10 (search for similar items in EconPapers)
Date: 1996
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-009-0263-3_8

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DOI: 10.1007/978-94-009-0263-3_8

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