Clone segments in Top and in Unif

Věra Trnková ()

A chapter in Categorical Topology, 1996, pp 249-268 from Springer

Abstract: Abstract Continuous and uniformly continuous maps of finite powers of metric spaces are investigated, e.g. for every 0 ≤ m ≤ n ≤ ∞, a metric space X is constructed such that the category of all continuous maps of the spaces X 0 = {ø}, X 1 = X, X 2 =X × X,…, X k and the category of all their uniformly continuous maps are: $$\begin{gathered} equal{\text{ }}exactly{\text{ }}when{\text{ }}\kappa \leqslant m{\mkern 1mu} {\text{ }}and \hfill \\ isomorphic{\text{ }}exactly{\text{ }}when{\text{ }}\kappa {\mkern 1mu} \leqslant {\mkern 1mu} {\text{ }}n. \hfill \\ \end{gathered} $$

Keywords: 08A40; 54C05; clones; products; continuous maps; uniformly continuous maps (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_23

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DOI: 10.1007/978-94-009-0263-3_23

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