Related papers: d-Boolean algebras and their bitopological represe…
In formal concept analysis, the collection of protoconcepts of any context forms a double Boolean algebra (dBa) which is fully contextual. Semiconcepts of a context form a pure dBa. The present article is a study on topological…
A duality between general partially ordered sets and certain topolgical spaces with two closures is established.
Harnessing the unimodular degree of freedom in the definition of any toric diagram, we present a method of constructing inequivalent gauge theories which are world-volume theories of D-branes probing the same toric singularity. These…
We dualize a construction of Aguzzoli-Flaminio-Ugolini of a large class of MTL-algebras from ordered quadruples consisting of a Boolean algebra, a generalized MTL-algebra, and two maps parameterizing the connection between these pieces. Our…
The notion of overlap algebra introduced by G. Sambin provides a constructive version of complete Boolean algebra. Here we first show some properties concerning overlap algebras: we prove that the notion of overlap morphism corresponds…
We construct Quillen equivalent semi-model structures on the categories of dg-Lie algebroids and $L_\infty$-algebroids over a commutative dg-algebra in characteristic zero. This allows one to apply the usual methods of homotopical algebra…
We introduce a notion of Q-algebra that can be considered as a generalization of the notion of Q-manifold (a supermanifold equipped with an odd vector field obeying {Q,Q} =0). We develop the theory of connections on modules over Q-algebras…
Duality groups of Abelian gauge theories on four manifolds and their reduction to two dimensions are considered. The duality groups include elements that relate different space-times in addition to relating different gauge-coupling…
Scaled Boolean algebras are a category of mathematical objects that arose from attempts to understand why the conventional rules of probability should hold when probabilities are construed, not as frequencies or proportions or the like, but…
By de Vries duality, the category of compact Hausdorff spaces is dually equivalent to the category of de Vries algebras. In our recent article, we have extended de Vries duality to completely regular spaces by generalizing de Vries algebras…
We show that the following five categories are equivalent: (1) the opposite category of commutative von Neumann algebras; (2) compact strictly localizable enhanced measurable spaces; (3) measurable locales; (4) hyperstonean locales; (5)…
It is well known that the variety of Boolean semirings, which is generated by the three element semiring S, is dual to the category of partially Stone spaces. We place this duality in the context of natural dualities. We begin by…
In [1] we introduced the concept of structured space, which is a topological space that locally resembles some algebraic structures. In [2] we proceeded the study of these spaces, developing two cohomology theories. The aim of this paper is…
We extend Makkai duality between coherent toposes and ultracategories to a duality between toposes with enough points and ultraconvergence spaces. Our proof generalizes and simplifies Makkai's original proof. Our main result can also be…
Let $A$ and $B$ be $C^*$-algebras with $A\subseteq M(B)$. Exploiting the duality between sober spaces and spatial locales, and the adjunction between restriction and induction for ideals in $A$ and $B$, we identify conditions that allow to…
We introduce the notion of an introverted Boolean algebra $\cal B$ of closed-and-open subsets of a topological group $G$, show that the associated Stone space $(\nu_{\cal B} G, \nu_{\cal B})$ is a totally disconnected semigroup…
String compactifications with T-duality twists are revisited and the gauge algebra of the dimensionally reduced theories calculated. These reductions can be viewed as string theory on T-fold backgrounds, and can be formulated in a `doubled…
We introduce the notion of an algebraic cocycle as the algebraic analogue of a map to an Eilenberg-MacLane space. Using these cocycles we develop a ``cohomology theory" for complex algebraic varieties. The theory is bigraded, functorial,…
We develop dualities for complete perfect distributive quasi relation algebras and complete perfect distributive involutive FL-algebras. The duals are partially ordered frames with additional structure. These frames are analogous to the…
We extend the $C^{\ast}-$algebraic formalism of Topological T-duality to section algebras of locally trivial bundles of strongly self-absorbing $C^{\ast}-$algebras and to a larger class of String Theoretic dualities. We argue that…