Topological methods in the study of functions with values in computation domains and fuzzy (quasi-)uniformities


Project supported by the Ministry of Education and Science of Spain

Grant number MTM2006-14925-C02-02

From October 1, 2006 until September 30, 2009


The members of the Research project are: Key words:
Publications:
  1. J. Gutiérrez García and Jorge Picado,
    On the algebraic representation of semicontinuity,
    J. Pure Appl. Algebra 210 (2007), no. 2, 299-306.

  2. J. Gutiérrez García, M.A. de Prada Vicente and S. Romaguera,
    Completeness on Hutton uniform spaces,
    Fuzzy Sets and Systems 158 (2007), no. 16, 1791-1802.

  3. J. Gutiérrez García
    Order-reversing involutions and lattices with residuation,
    Indian Journal of Pure and Applied Mathematics 38 (2007), no. 4, 271-280

  4. I. Mardones Pérez and M.A. de Prada Vicente,
    Monotone insertion of lattice-valued functions,
    Acta Math. Hung. 117 (2007), no. 1-2, 187-200.

  5. J. Gutiérrez García and T. Kubiak,
    Sandwich-type characterization of completely regular spaces,
    Applied General Topology 8 (2007), no. 2, 239-242.

  6. J. Gutiérrez García, M.A. de Prada Vicente and T. Kubiak,
    Generating and inserting continuous functions with values in bounded complete domains and hedgehog-like structures,
    Houston J. Math. 34 (2008), no. 1, 123-144.

  7. J. Gutiérrez García, T. Kubiak and Jorge Picado,
    Monotone insertion and monotone extension of frame homomorphisms,
    J. Pure Appl. Algebra 212 (2008), no. 5, 955-968.

  8. J. Gutiérrez García and T. Kubiak,
    A new look at some classical theorems on continuous functions on normal spaces,
    Acta Mathematica Hungarica 119 (2008), no. 4, 333-339.

  9. J. Gutiérrez García, I. Mardones Pérez, J. Picado and M.A. de Prada Vicente,
    Uniform-type structures on lattice-valued spaces and frames,
    Fuzzy Sets and Systems 159 (2008), no. 19, 2469-2487.

  10. U. Höhle and T. Kubiak,
    Approximating orders in meet-continuous lattices and regularity axioms in many valued topology,
    Order 25 (2008), no. 1, 9-17.

  11. U. Höhle and T. Kubiak,
    A note on Hausdorff separation in $L$-$\mathbf{Top}$,
    Fuzzy Sets and Systems 159 (2008), no. 19, 2606-2610.

  12. J. Gutiérrez García, T. Kubiak and J. Picado,
    Pointfree forms of Dowker and Michael insertion theorems,
    J. Pure Appl. Algebra. 213 (2009), no. 1, 98-108.

  13. J. Gutiérrez García, I. Mardones Pérez and M.A. de Prada Vicente,
    Monotone normality free of T1 axiom,
    Acta Math. Hungar., 122 (2009), no. 1-2, 71-80.

  14. J. Gutiérrez García, T. Kubiak and J. Picado,
    Lower and upper regularizations of frame semicontinuous real functions,
    Algebra univers. 60 (2009), no. 2, 169-184.

  15. J. Gutiérrez García, T. Kubiak and J. Picado,
    Localic real functions: a general setting,
    J. Pure Appl. Algebra 213 (2009), no. 6, 1064-1074.

  16. T. Kubiak and M.A. de Prada Vicente,
    On quasi-uniform space valued semi-continuous functions,
    Comment. Math. Univ. Carolin. 50 (2009), no. 1, 125-133.

  17. J.C. Candeal, J. Gutiérrez García and E. Indurain,
    Universal codomains to represent interval-orders,
    International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 17 (2009), no. 1, 197-219.

  18. J. Gutiérrez García, M.A. de Prada Vicente and T. Kubiak,
    Controlling disjointness with a hedgehog,
    Houston J. Math. 35 (2009), no. 2, 469-484

  19. G. Bosi, J. Gutiérrez García and E. Induráin
    Unified representability of total preorders and interval orders through a single function: The lattice approach,
    Order 26 (2009), no. 3, 255-275.

  20. M.J. Ferreira, J. Gutiérrez García and J. Picado,
    Completely normal frames and real-valued functions,
    Topology Appl.156 (2009), 2932-2941.

  21. J. Gutiérrez García, Iraide Mardones Pérez, M.A. de Prada Vicente and Dexue Zhang,
    Fuzzy Galois connections categorically,
    Mathematical Logic Quarterly 2 (2010), 131-147..

  22. J. Gutiérrez García, S. Romaguera and M. Sanchis
    Fuzzy uniform structures and continuous $t$-norms,
    Fuzzy Sets and Systems 161 (2010), 1011-1021.
Conferences:
  1. J. Gutiérrez García, (coauthors T. Kubiak and M.A. de Prada Vicente),
    Insertion and extension of hedgehog-valued functions,
    22nd Summer Conference on Topology and Its Applications, Castellón, Spain. July 2007.

  2. M.A. de Prada Vicente, (coauthor T. Kubiak),
    On quasi-uniform space valued semicontinuous functions,
    22nd Summer Conference on Topology and Its Applications, Castellón, Spain. July 2007.

  3. I. Mardones Pérez, (coauthors J. Gutiérrez García, M.A. de Prada Vicente and Jorge Picado),
    Uniform-type structures on lattice-valued spaces and frames,
    22nd Summer Conference on Topology and Its Applications, Castellón, Spain. July 2007.

  4. J. Gutiérrez García, (coauthors Juan Carlos Candeal and Esteban Induráin),
    Universal codomains to represent interval orders,
    22nd Summer Conference on Topology and Its Applications, Castellón, Spain. July 2007.

  5. J. Gutiérrez García, (coauthors T. Kubiak and J. Picado),
    Localic real-valued functions: a general setting,
    29th Linz Seminar on Fuzzy Set Theory: Foundations of Lattice-Valued Mathematics with Applications to Algebra and Topology, Linz, Austria. February 2008.
    (Invited speaker)

  6. I. Mardones Pérez, (coauthors J. Gutiérrez García, M.A. de Prada Vicente and Jorge Picado),
    Uniform-type structures on lattice-valued spaces and frames,
    29th Linz Seminar on Fuzzy Set Theory: Foundations of Lattice-Valued Mathematics with Applications to Algebra and Topology, Linz, Austria. February 2008.

  7. T. Kubiak, (coauthors J. Gutiérrez García and M.A. de Prada Vicente),
    Controlling disjointness with a hedgehog,
    Set Theory, Topology and Banach Spaces (Second International Topology Conference in Kielce), Kielce, Poland. July 2008.

  8. J. Gutiérrez García, (coauthors T. Kubiak and J. Picado),
    Making the ring of continuous localic real functions into a subring of all localic real functions,
    BLAST 2008, Denver, USA. August 2008.

  9. I. Mardones Pérez, (coauthors J. Gutiérrez García and M.A. de Prada Vicente),
    Insertion Theorems for Lattice-valued Functions on Preordered Topological Spaces,
    (Invited speaker)

    10. Workshop in Applied Topology (WiAT'09), Palma de Mallorca, Spain, June 2009.
  10. M.A. de Prada Vicente,
    From the real numbers to domains,
    Workshop in Applied Topology (WiAT'09), Palma de Mallorca, Spain, June 2009.
    (Invited speaker)

  11. J. Gutiérrez García, (coauthor Esteban Induráin),
    Unified representability of total preorders, semiorders and interval orders through scales and a single map,
    (Invited speaker)

    12. Workshop in Applied Topology (WiAT'09), Palma de Mallorca, Spain, June 2009.
  12. J. Gutiérrez García, (coauthor Tomasz Kubiak),
    Localic analogues of general insertion and extension theorems for real-valued functions,
    International Category Theory Conference 2009 (CT2009), Cape Town, South Africa, June-July 2009.

  13. J. Gutiérrez García, (coauthors Tomasz Kubiak and Jorge Picado),
    Real-valued functions in pointfree topology,
    2nd International Conference on Topology and its Applications, Ankara,Turkey, July 2009.
    (Invited speaker)

  14. Tomasz Kubiak, (coauthor J. Gutiérrez García),
    Embedding locales of prescribed weight into localic products,
    24th Summer Conference on Topology and Its Applications, Brno,Czeck Republic, July 2009.

  15. J. Gutiérrez García, (coauthor Jorge Picado),
    On extended real valued functions in pointfree topology,
    VI Portuguese Category Seminar, Coimbra, Portugal, July, 2009.
    (Invited speaker)