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We consider all compatible topologies of an arbitrary finite-dimensional vector space over a non-trivial valuation field whose metric completion is a locally compact space. We construct the canonical lattice isomorphism between the lattice…

General Topology · Mathematics 2023-12-01 Takanobu Aoyama

Let $\Cc$ and $\Dd$ be two corings over a ring $A$ and $\Cc\stackrel{\lambda}{\longrightarrow}\Dd$ be a morphism of corings. We investigate the situation when the associated induced ("corestriction of scalars") functor…

Quantum Algebra · Mathematics 2007-05-23 Miodrag C. Iovanov

Category theory gives a mathematical characterization of naturality but not of canonicity. The purpose of this paper is to develop the logical theory of canonical maps based on the broader demonstration that the dual notions of elements &…

Category Theory · Mathematics 2024-10-07 David Ellerman

We study the question of local and global uniqueness of completions, based on null geodesics, of Lorentzian manifolds. We show local uniqueness of such boundary extensions. We give a necessary and sufficient condition for existence of…

General Relativity and Quantum Cosmology · Physics 2007-05-23 Piotr T. Chruściel

We introduce the formal extension of the Whitney functor and the polynomial extension of the tempered cohomology functor, and prove a natural topological duality between them.

Algebraic Geometry · Mathematics 2011-06-23 Ana Rita Martins , Teresa Monteiro Fernandes

We connect Priestley duality for distributive lattices and its generalization to distributive meet-semilattices to Hofmann-Mislove-Stralka duality for semilattices. Among other things, this involves consideration of various morphisms…

Logic · Mathematics 2024-11-25 Guram Bezhanishvili , Luca Carai , Patrick Morandi

We establish the action of three-dimensional bosonization and particle-vortex duality in the presence of a boundary, which supports a non-anomalous two-dimensional theory. We confirm our prescription using a microscopic realization of the…

High Energy Physics - Theory · Physics 2018-04-04 Kyle Aitken , Andrew Baumgartner , Andreas Karch , Brandon Robinson

We prove the canonicity of inductive inequalities in a constructive meta-theory, for classes of logics algebraically captured by varieties of normal and regular lattice expansions. This result encompasses Ghilardi-Meloni's and Suzuki's…

Logic · Mathematics 2023-06-22 Willem Conradie , Alessandra Palmigiano

We construct topological defects in two-dimensional classical lattice models and quantum chains. The defects satisfy local commutation relations guaranteeing that the partition function is independent of their path. These relations and…

Statistical Mechanics · Physics 2020-08-21 David Aasen , Paul Fendley , Roger S. K. Mong

We introduce new modified Abelian lattice models, with inhomogeneous local interactions, in which a sum over topological sectors are included in the defining partition function. The dual models, on lattices with arbitrary topology, are…

High Energy Physics - Theory · Physics 2008-11-26 Sebastian Jaimungal

We prove an algebraic canonicity theorem for normal LE-logics of arbitrary signature, in a generalized setting in which the non-lattice connectives are interpreted as operations mapping tuples of elements of the given lattice to closed or…

Logic · Mathematics 2021-02-23 Laurent De Rudder , Alessandra Palmigiano

We develop a new duality for distributive and implicative meet semi-lattices. For distributive meet semi-lattices our duality generalizes Priestley's duality for distributive lattices and provides an improvement of Celani's duality. Our…

Logic · Mathematics 2024-11-01 Guram Bezhanishvili , Ramon Jansana

The ordering relation of a bounded distributive lattice L is a (distributive) (0, 1)-sublattice of L \times L. This construction gives rise to a functor \Phi from the category of bounded distributive lattices to itself. We examine the…

Logic · Mathematics 2007-05-29 Michel Krebs , Dominic van der Zypen

The canonical involution of a double (=iterated) tangent bundle may be dualized in different ways to yield relations between the Tulczyjew diffeomorphism, the Poisson anchor associated with the standard symplectic structure on the cotangent…

Differential Geometry · Mathematics 2007-05-23 K. C. H. Mackenzie

Dualization of a monotone Boolean function on a finite lattice can be represented by transforming the set of its minimal 1 to the set of its maximal 0 values. In this paper we consider finite lattices given by ordered sets of their meet and…

Logic in Computer Science · Computer Science 2015-12-31 Mikhail A. Babin , Sergei O. Kuznetsov

We establish the generalized canonical bundle formula for generalized lc-trivial fibrations with irrational coefficients over non-compact bases in the complex analytic setting, and we show that the discriminant b-divisor and moduli…

Algebraic Geometry · Mathematics 2026-05-05 Kenta Hashizume

This book is a course in Stone-Priestley duality theory, with applications to logic and theoretical computer science. Our target audience are graduate students and researchers in mathematics and computer science. Our aim is to get in a…

Logic · Mathematics 2023-04-06 Mai Gehrke , Sam van Gool

Given a p-form defined on the smooth locus of a normal variety, and a resolution of singularities, we study the problem of extending the pull-back of the p-form over the exceptional set of the desingularization. For log canonical pairs and…

Algebraic Geometry · Mathematics 2019-02-20 Daniel Greb , Stefan Kebekus , Sándor J. Kovács

This paper deals with extension of analytic covers. We prove topological extension theorems for analytic covers. The main result is an extension theorem which only uses the extension of the ramification divisor. We give also a Thullen-type…

Complex Variables · Mathematics 2016-04-28 Landry Lavoine

This paper fills a gap in the literature on natural duality theory. It concerns dual representations of categories of distributive-lattice-based algebras in which the lattice reducts are not assumed to have bounds. The development of theory…

Rings and Algebras · Mathematics 2020-02-18 Leonardo M. Cabrer , Hilary A. Priestley