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The complexity (quasi-metric) space has been introduced as a part of the development of a topological foundation for the complexity analysis of algorithms ([12]). Applications of this theory to the complexity analysis of Divide & Conquer algorithms have been discussed in [12]. Here we obtain several quasi-metric properties of the complexity space. The main… (More)

- Jesús Rodríguez-López, Salvador Romaguera
- Fuzzy Sets and Systems
- 2004

We propose a method for constructing a Hausdor$ fuzzy metric on the set of the nonempty compact subsets of a given fuzzy metric space (in the sense of George and Veeramani). We discuss several important properties as completeness, completion and precompactness. Some illustrative examples are given. c © 2003 Elsevier B.V. All rights reserved. MSC: 54A40;… (More)

- Valentín Gregori, Salvador Romaguera
- Fuzzy Sets and Systems
- 2000

The complexity (quasi-metric) space was introduced in [23] to study complexity analysis of programs. Recently, it was introduced in [22] the dual complexity (quasi-metric) space, as a subspace of the function space [0,+∞)ω. Several quasi-metric properties of the complexity space were obtained via the analysis of its dual. We here show that the structure of… (More)

- Carmen Alegre, Salvador Romaguera
- Fuzzy Sets and Systems
- 2010

- Valentín Gregori, Salvador Romaguera
- Fuzzy Sets and Systems
- 2002

Completions of fuzzy metric spaces (in the sense of George and Veeramani) are discussed. A complete fuzzy metric space Y is said to be a fuzzy metric completion of a given fuzzy metric space X if X is isometric to a dense subspace of Y . We present an example of a fuzzy metric space that does not admit any fuzzy metric completion. However, we prove that… (More)

Stable partial metric spaces (or the equivalent invariant weightable quasi-metric spaces) form a fundamental concept in Quantitative Domain Theory. Indeed, all domains have been shown to be quantifiable via a stable partial metric (e.g. [22], [23], [26]). Monoid operations arise in Domain Theory in the context of power domains. These operations also arise… (More)

- Salvador Romaguera, Michel P. Schellekens
- Electr. Notes Theor. Comput. Sci.
- 2000

In [Sch00] a bijection has been established, for the case of semilattices, between invariant partial metrics and semivaluations. Semivaluations are a natural generalization of valuations on lattices to the context of semilattices and arise in many different contexts in Quantitative Domain Theory ([Sch00]). Examples of well known spaces which are… (More)

Article history: Received 16 April 2008 Available online 16 July 2008 Submitted by B. Cascales