w_Estructuras ordenadas y Topología

Ordered structures and topology


Department (s)
Mathematics, Applied economics I

Knowledge area
PI: Javier Gutiérrez García Co-PI:


UPV/EHU: Igor Arrieta Torres,  Javier Gutiérrez García, Iraide Mardones Pérez, Imanol Mozo Carollo
Non UPV/EHU: Ulrich Höhle (Germany), Tomasz Kubiak (Poland), Jorge Picado (Portugal), Ales Pultr (Czech Republic)


Pointfree topology, many-valued topology, non-commutative topology,


Our research is devoted to the study of different topics in the general field of ordered structures and topology. The most relevant topics are the following: 
Topics on pointfree topology: Pointfree topology is a well-established area of study of what is usually called Categorical Topology. It is a modern algebraic approach to Topology on a constructive foundation.
Topics on many-valued and non-commutative topology: Many-valued topology is motivated by topological structures which cannot be represented by traditional two-valued topologies. When the complete lattice of truth values L is also a semigroup with a not necessarily commutative binary operation, non-commutative many valued topology arises

Lines of Research

  1. Pointfree Topology: The lattice of sublocales; Localic real-valued functions and variants; Structured frames; Special properties in frames; Applications.
  2.  Many-valued topology: L-topological properties of the newly introduced tensor product (M⊗L) endowed with its interval L-topology; Katetov insertion theorem for continuous (M⊗L) -valued functions; Adjointness between the categories Unif(M⊗L) and Unif(L).
  3.  Non-commutative topology: Developments of basic concepts of enriched topology; Enriched topologies on enriched order structures; The topological investigation of spectra of non-commutative C*-algebras; Gelfand-Naimark-Theorem for non-commutative C*-algebras.


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