The most relevant topics and the proposed objectives in this project are the following:

1. (i) Study of the completion of the Hausdorff fuzzy metric of a fuzzy metric space, with application to the classical
metric framework and to the extension of contractive multifunctions, including the case of dynamical systems. (ii)
Definition and systematized study of a suitable notion of Wijsman topology for fuzzy metric spaces. Applications.
(iii) Characterization of the supremum metric by means of uniform convergence and study of the extension of this
concept to the uniform framework. (iv) Obtaining fixed point theorems for multivalued mappings on quasi-metric
(hyper)spaces with the help of w-distances. (v) Application of fuzzy metrics to the robust filtering of colour images.
Revision of the theory of duality in fuzzy normed spaces.

2. Construction of quantitative domains of computations of Waszkiewicz type for the Sorgenfrey quasimetric
and the quasi-metric of the domain of words, and for uniform spaces, in terms of formal balls.

3. (i) Study of functions with values in a bounded complete domain. In particular, we tackle the study of insertion
and extension of functions. (ii) Relationship between functions with values in the interval domain and functions
with values in the set of fuzzy real numbers. (iii) Analysis of the existence of numerical representations of ordered
structures, in particular interval orders and semiorders in both the usual and the fuzzy setting.

4. (i) To pursue the development of the theory of pointfree real-valued functions, with the investigation of questions
related with insertion and extension of functions. (ii) Study of partial real numbers (the interval domain) from a
pointfree point of view, and its connections with the theory of domains and the work on constructive integration.
(iii) To look for insertion theorems in uniform frames and their connections with metrization theorems in a pointfree
setting.