相关论文: The history of three wrong definitions
This is a survey of the author's recent results on the Kadison and Halmos similarity problems and the closely connected notion of ``length'' of an operator algebra.
Refinements of some recent reverse inequalities for the celebrated Cauchy-Bunyakovsky-Schwarz inequality in 2-inner product spaces are given. Using this framework, applications for determinantal integral inequalities are also provided.
A metric relation by definition is symmetric. Since many data sets are non-symmetric, in this paper we develop a systematic theory of non-symmetric cost functions. Betweenness relations play an important role. We also introduce the notion…
We introduce an analogue of the theory of length spaces into the setting of Lorentzian geometry and causality theory. The r\^ole of the metric is taken over by the time separation function, in terms of which all basic notions are…
The intention of this article is to give a flavour of some global problems in General Relativity. We cover a variety of topics, some of them related to the fundamental concept of 'Cauchy hypersurfaces': (1) structure of globally hyperbolic…
In a metric space $M=(X,d)$, we say that $v$ is between $u$ and $w$ if $d(u,w)=d(u,v)+d(v,w)$. Taking all triples $\{u,v,w\}$ such that $v$ is between $u$ and $w$, one can associate a 3-uniform hypergraph with each finite metric space $M$.…
This is a write-up of a talk given at the CATMI meeting in Bergen in July 2023, and is an introduction to a category-theoretic perspective on metric spaces. A metric space is a set of points such that between each pair of points there is a…
The concept of complexity appears in virtually all areas of knowledge. Its intuitive meaning shares similarities across fields, but disagreements between its details hinders a general definition, leading to a plethora of proposed…
In this paper we consider partial metric spaces in the sense of O'Neill. We introduce the notions of strong partial metric spaces and Cauchy functions. We prove a fixed point theorem for such spaces and functions that improves Matthews'…
19th century real analysis received a major impetus from Cauchy's work. Cauchy mentions variable quantities, limits, and infinitesimals, but the meaning he attached to these terms is not identical to their modern meaning. Some Cauchy…
Metric regularity has emerged during last 2-3 decades as one of the central concepts of variational analysis. The roots of this concept go back to a circle of fundamental regularity ideas of classical analysis embodied in such results as…
Categories enriched in the opposite poset of non-negative reals can be viewed as generalizations of metric spaces, known as Lawvere metric spaces. In this article, we develop model structures on the categories…
This is an extended survey of the results concerning a hierarchy of languages that is tightly connected with the quantifier alternation hierarchy within the two-variable fragment of first order logic of the linear order.
The arising of central extensions is discussed in two contexts. At first classical counterparts of quantum anomalies (deserving being named as "classical anomalies") are associated with a peculiar subclass of the non-equivariant maps.…
In a metric space, such as the real numbers with their standard metric, a set A is open if and only if no sequence with terms outside of A has a limit inside A. Moreover, a metric space is compact if and only if every sequence has a…
The topic of "negative end" of change is, contrary to the fields of innovation and emergence, largely under-researched. Yet, it has lately started to gain an increasing attention from language scholars worldwide. The main focus of this…
Many systems of interest to control engineering can be modeled by linear complementarity problems. We introduce a new notion of equivalence between linear complementarity problems that sets the basis to translate the powerful tools of…
In this paper we have studied the notion of rough convergence of sequences in a partial metric space. We have also investigated how far several relevant results on boundedness, rough limit sets etc. which are valid in a metric space are…
Prior work of Gavryushkin, Khoussainov, Jain and Stephan investigated what algebraic structures can be realised in worlds given by a positive (= recursively enumerable) equivalence relation which partitions the natural numbers into…
Ontologies have been used for the purpose of bringing system and consistency to subject and knowledge areas. We present a criticism of the present mathematical structure of ontologies and indicate that they are not sufficient in their…