Related papers: A metric-like topology yon BL-algebras
We show that certain spaces of log-integrable functions and operators are complete topological *-algebras with respect to a natural metric space structure. We explore connections with the Nevanlinna class of holomorphic functions.
The efficiency of contemporary algebraic topology is not optimal since the category of topological spaces can be made more algebraic by introducing a profoundly new (-1)-dimensional topological space as a topological join unit. Thereby…
The Lie algebra $gl(V)$ is the Lie algebra of all endomorphisms of a countable-dimensional complex vector space $V$. We define a tensor category of topological representations of the Lie algebra $gl(V)$, so that $V$, its dual and the…
There are many examples of dualities between topological spaces and algebras in the literature. Particularly, many of those examples come from the algebraic counterpart of a logical system, e.g, boolean and heyting algebras, MV-algebras,…
Barycentric algebras are an abstraction of the notion of convex sets, defined by a set of equations. We study semitopological and topological barycentric algebras, in the spirit of a previous study by Klaus Keimel on semitopological and…
A Boolean algebra $\A$ equipped with a (finitely-additive) positive probability measure $m$ can be turned into a metric space $(\A , d_{m})$, where $d_{m}(a,b)= m ((a\wedge\neg b)\vee(\neg a\wedge b))$, for any $a,b\in A$, sometimes…
The main goal of this article is to introduce BL-rings, i.e., commutative rings whose lattices of ideals can be equipped with a structure of BL-algebra. We obtain a description of such rings, and study the connections between the new class…
Given an associative, not necessarily commutative, ring R with identity, a formal matrix calculus is introduced and developed for pairs of matrices over R. This calculus subsumes the theory of homogeneous systems of linear equations with…
The study of topological information of spatial objects has for a long time been a focus of research in disciplines like computational geometry, spatial reasoning, cognitive science, and robotics. While the majority of these researches…
We define a basic class of algebras which we call homotopy path algebras. We find that such algebras always admit a cellular resolution and detail the intimate relationship between these algebras, stratifications of topological spaces, and…
Thurston introduced in his seminal work an asymmetric metric on Teichm\"uller space by the ratio of simple closed curve length. In this paper, we generalize the idea and define an asymmetric metric on the space of unit-area flat metrics…
In Part I of this paper, we introduced a class of certain algebras of finite dimension over a field. All these algebras are split, symmetric and local. Here we continue to investigate their Loewy structure. We show that in many cases their…
In this paper we introduce and study so-called $k^*$-metrizable spaces forming a new class of generalized metric spaces, and display various applications of such spaces in topological algebra, functional analysis, and measure theory. By…
We introduce a type $B$ analogue of the nil Temperley-Lieb algebra in terms of generators and relations, that we call the (extended) nil-blob algebra. We show that this algebra is isomorphic to the endomorphism algebra of a Bott-Samelson…
A host algebra of a topological group G is a C^*-algebra whose representations are in one-to-one correspondence with certain continuous unitary representations of G. In this paper we present an approach to host algebras for infinite…
Consider the semialgebraic structure over the real field. More generally, let an ominimal structure be over a real closed field. We show that a definable metric space X with a definable metric d is embedded into a Euclidean space so that…
In this work we consider all metric Lie algebras, having a nondegenerate symmetric invariant bilinear form, over \C and \R up to dimension 5 and all metric Lie algebras over \C in dimension 6. We introduce cyclic and reduced cyclic…
We consider the space of linear maps from a coassociative coalgebra C into a Lie algebra L. Unless C has a cocommutative coproduct, the usual symmetry properties of the induced bracket on Hom(C,L) fail to hold. We define the concept of…
Through the subsequent discussion we consider a certain particular sort of (topological) algebras, which may substitute the `` structure sheaf algebras'' in many--in point of fact, in all--the situations of a geometrical character that…
This article belongs to a subject, Directed Algebraic Topology, whose general aim is including non-reversible processes in the range of topology and algebraic topology. Here, as a further step, we also want to cover "critical processes",…