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Realization of Cartesian closed topological hulls. (English) Zbl 0573.54006

The Cartesian closed topological (CCT) hull of a concrete category K is the smallest full CCT extension of K. The existence of a CCT hull for Top was established by P. Antoine [Bull. Soc. Math. Belg. 18, 142-264 and 387-414 (1966; Zbl 0158.199 and Zbl 0192.101)]; this was also studied by A. Machado [Cah. Topologie Géom. Différ. 14, 309-327 (1973; Zbl 0276.54001)] and G. Bourdaud [ibid. 16, 107-133 (1975; Zbl 0315.54005) and Lect. Notes Math. 540, 93-108 (1976)]. This paper examines the general question of the existence of CCT hulls for the following examples of K: topological spaces, uniform spaces, pre- topological spaces, compact \(T_ 2\)-spaces, metrizable spaces and completely regular spaces. Most of these examples have been studied before but the identification of the category of functionally sequential topological spaces as the CCT hull of the category of metrizable spaces, is new.
Reviewer: T.Porter

MSC:

54B30 Categorical methods in general topology
18B30 Categories of topological spaces and continuous mappings (MSC2010)
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References:

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