Applied Categorical Structures

, Volume 21, Issue 6, pp 617–650 | Cite as

Approaching Metric Domains

  • Gonçalo Gutierres
  • Dirk HofmannEmail author


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.


Continuous lattice Metric space Approach space Injective space Cocomplete space 

Mathematics Subject Classifications (2010)

06B35 18B35 18B30 54A05 54E35 


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© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.CMUC, Department of MathematicsUniversity of CoimbraCoimbraPortugal
  2. 2.Center for Research and Development in Mathematics and Applications, Department of MatematicsUniversity of AveiroAveiroPortugal

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