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Approaching Metric Domains

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Abstract

In analogy to the situation for continuous lattices which were introduced by Dana Scott as precisely the injective T0 spaces via the (nowadays called) Scott topology, we study those metric spaces which correspond to injective T0 approach spaces and characterise them as precisely the continuous lattices equipped with a unitary and associative [0, ∞ ]-action. This result is achieved by a detailed analysis of the notion of cocompleteness for approach spaces.

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Authors and Affiliations

  1. CMUC, Department of Mathematics, University of Coimbra, 3001-454, Coimbra, Portugal

    Gonçalo Gutierres

  2. Center for Research and Development in Mathematics and Applications, Department of Matematics, University of Aveiro, 3810-193, Aveiro, Portugal

    Dirk Hofmann

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  1. Gonçalo Gutierres
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  2. Dirk Hofmann
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Correspondence to Dirk Hofmann.

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Gutierres, G., Hofmann, D. Approaching Metric Domains. Appl Categor Struct 21, 617–650 (2013). https://doi.org/10.1007/s10485-011-9274-z

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