Research
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
[11] The patch topology in univalent foundations
(joint with Martín H. Escardó and Ayberk Tosun)
Submitted (2024).
PUBLICATIONS
[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
RECENT TALKS AND SLIDES
Below you may find a list of some of my recent talks.
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