RESEARCH INTERESTS
Point-free topology or locale theory: separation axioms, closure operators, insertion and extension of functions, rings of real-valued functions, Stone-type dualities, uniform structures, metric structures and metric diameters, generalizations of normality, subobject lattices, constructive locale theory.
Quantales: quantale-enriched categories, in particular quantale-enriched topological spaces.
More generally, I like using categorical and algebraic methods in topology.
PREPRINTS
[14] The lattice of smooth sublocales as a Bruns-Lakser completion
(joint with Anna Laura Suarez)
Submitted (2026).
PUBLICATIONS
[13] Joins of closed sublocales are not always a coframe
Order 43 (2026).
[12] The patch topology in univalent foundations
(joint with Martín H. Escardó and Ayberk Tosun)
Mathematical Structures in Computer Science 35 (2025).
[11] The DeMorganization of a locale
Annals of Pure and Applied Logic 176 (2025).
[10] Localic separation and the duality between closedness and fittedness
Topology and its Applications 342 (2024).
[9] Notes on the spatial part of a frame
(joint with Jorge Picado and Aleš Pultr)
Categories and General Algebraic Structures with Applications 20 (2024).
Preprint 23-12 DMUC
[8] Enriched lower separation axioms and the principle of enriched continuous extension
(joint with Javier Gutiérrez García and Ulrich Höhle)
Fuzzy Sets and Systems 468 (2023).
[7] On the categorical behaviour of D-localic maps
(joint with Javier Gutiérrez García).
Quaestiones Mathematicae 46 (2023).
Preprint 21-50 DMUC
[6] Frame presentations of compact hedgehogs and their properties
(joint with Javier Gutiérrez García and Jorge Picado).
Quaestiones Mathematicae 46 (2023).
Preprint 21-26 DMUC
[5] A general insertion theorem for uniform locales
(joint with Ana Belén Avilez),
Journal of Pure and Applied Algebra 227 (2023).
Preprint 22-20 DMUC
[4] On joins of complemented sublocales
Algebra Universalis 83 (2022).
Preprint 20-23 DMUC
[3] A new diagonal separation and its relations with the Hausdorff property
(joint with Jorge Picado and Aleš Pultr),
Applied Categorical Structures 30 (2022).
Preprint 21-17 DMUC
[2] The coframe of D-sublocales and the TD-duality
(joint with Anna Laura Suarez),
Topology and its Applications 291 (2021).
Preprint 20-34 DMUC
[1] On infinite variants of De Morgan law in locale theory
Journal of Pure and Applied Algebra 225 (2021).
Preprint 20-03 DMUC
COLLABORATORS
Marco Abbadini
Rodrigo N. Almeida
Ana Belén Avilez
Martín H. Escardó
Javier Gutiérrez García
Ulrich Höhle
Jorge Picado
Aleš Pultr
Anna Laura Suarez
Ayberk Tosun
RECENT TALKS AND SLIDES
Below you may find a list of some of my recent talks.
VIII SMLS. The DeMorganization of a locale.
A day on Pointfree Topology - celebrating Jorge Picado's 60th birthday, Revisiting localic T1-type separation. Slides.
AMS Fall Central Sectional Meeting 2022, A cardinal generalization of normality and the frame of the compact hedgehog.
TACT 2022, A general insertion theorem for uniform locales.
TACL 2022, Generalized subspaces in the duality of TD-spaces. Slides.
THESES
PhD thesis
A study of localic subspaces, separation, and variants of normality and their duals (available here).
Supervisors: Javier Gutiérrez García and Jorge Picado.
Master thesis
Part III essay : Categories of relations.
Supervisor: Peter Johnstone
Bachelor thesis
A tale of three hedgehogs. (available at the repository of UPV/EHU or in arXiv).
Supervisors: Jon González-Sánchez and Javier Gutiérrez García