Related papers: Functorial maps and weak parities
In this paper, we point out that the definition of weak tracial approximation can be improved and strengthened. An example of weak tracial approximation is also provided.
In functional analysis it is well known that every linear functional defined on the dual of a locally convex vector space which is continuous for the weak topology is the evaluation at a uniquely determined point of the given vector space.…
In this paper, we introduce the new concepts of subcompatibility and subsequential continuity which are respectively weaker than occasionally weak compatibilty and reciprocal continuity. With them, we establish several common fixed point…
Two natural generalizations of knot theory are the study of spatially embedded graphs, and Kauffman's theory of virtual knots. In this paper we combine these approaches to begin the study of virtual spatial graphs.
Network appliances perform different functions on network flows and constitute an important part of an operator's network. Normally, a set of chained network functions process network flows. Following the trend of virtualization of…
In planar maximally supersymmetric Yang-Mills, we can compute three-point functions at weak coupling using the so-called hexagonalization formalism. The main objects in this framework are called hexagons. We are interested in two sectors of…
In this paper, inspired by the concept of generalized weakly contractive mappings in metric spaces, we introduce C-Class function and fixed point theory for weakly contractive in the setting of rectangular $b$-metric spaces and established…
A theorem of Davis, Figiel, Johnson and Pe{\l}czy\'nski tells us that weakly-compact operators between Banach spaces factor through reflexive Banach spaces. The machinery underlying this result is that of the real interpolation method,…
We introduce a new technique for studying classical knots with the methods of virtual knot theory. Let $K$ be a knot and $J$ a knot in the complement of $K$ with $\text{lk}(J,K)=0$. Suppose there is covering space $\pi_J: \Sigma \times…
This paper addresses weak approximation for rationally connected varieties defined over the function field of a curve, especially at places of bad reduction. Our approach entails analyzing the rational connectivity of the smooth locus of…
We establish common fixed point theorems for two pairs of weakly compatible self-mappings using an auxiliary function of two variables. Unlike classical results, our theorems do not assume continuity of the mappings and require completeness…
Frieze patterns form a nexus between algebra, combinatorics, and geometry. T-paths with respect to triangulations of surfaces have been used to obtain expansion formulae for cluster variables. This paper will introduce the concepts of weak…
Weak structures abound in higher category theory, but are often suitably equivalent to stricter structures that are easier to understand. We extend strictification for tricategories and trihomomorphisms to trinatural transformations,…
A phantom map is a potentially nontrivial map which induces the zero map on every homology theory and on homotopy groups. Zabrodsky has shown that in the presence of particular finiteness conditions on spaces $X$ and $Y$ every map $X\to Y$…
A virtual knot that has a homologically trivial representative $\mathscr{K}$ in a thickened surface $\Sigma \times [0,1]$ is said to be an almost classical (AC) knot. $\mathscr{K}$ then bounds a Seifert surface $F\subset \Sigma \times…
A classical approach for surface classification is to find a compact algebraic representation for each surface that would be similar for objects within the same class and preserve dissimilarities between classes. We introduce Self…
We prove functorial weak factorization of projective birational morphisms of regular quasi-excellent schemes in characteristic 0 broadly based on the existing line of proof for varieties. From this general functorial statement we deduce…
In this survey, I suggest to approach the problem of functorial properties of quantum cohomology by drawing lessons from several versions of Mirror duality involving deformation spaces.
In this note, we provide some categorical perspectives on the relativization construction arising from quantum measurement theory in the presence of symmetries and occupying a central place in the operational approach to quantum reference…
In this paper we combine a survey of the most important topological properties of kinematic maps that appear in robotics, with the exposition of some basic results regarding the topological complexity of a map. In particular, we discuss…