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We present a unified framework for categorical systems theory which packages a collection of open systems, their interactions, and their maps into a symmetric monoidal loose right module of systems over a symmetric monoidal double category…
We study continuity and boundedness of order-to-topology bounded and order-to topology continuous operators from ordered to topological vector spaces. Several results on automatic continuity of operators from ordered Frechet spaces to…
We describe how self-adjoint ordered operator spaces, also called non-unital operator systems in the literature, can be understood as $*$-vector spaces equipped with a matrix gauge structure. We explain how this perspective has several…
The aim of this paper is to explain the relationship between the (co)homology of the free loop space and the Hochschild homology of its singular cochain algebra. We introduce all the relevant technical tools, namely simplicial and cyclic…
We give a topological interpretation of the free metabelian group, following the plan described in [Ver1,Ver2]. This interpretation is based on considering the Caley graph of a finitely generated group G as one-dimensional complex; its…
In this work, we define new sequence spaces by combining generalized weighted mean and difference operator. Afterward, we investigate topological structure which are completeness, AK-property, AD-property. Also, we compute the alpha, beta…
We introduce a new definition of topological degree for a meaningful class of operators which need not be continuous. Subsequently, we derive a number of fixed point theorems for such operators. As an application, we deduce a new existence…
We give explicit descriptions of all path connected components and isolated points of both spaces of composition operators and nonzero weighted composition operators acting from a Fock space $\mathcal{F}^p(\mathbb{C}^n)$ to another one…
In this paper we will study the representations of isomorphisms between bases of topological spaces. It turns out that the perfect setting for this study is that of regular open subsets of complete metric spaces, but we have achieved some…
In this paper we initiate the study of real operator monotonicity for functions of tuples of operators, which are multivariate structured maps with a functional calculus called free functions that preserve the order between real parts (or…
Chas and Sullivan have defined an intersection-type product on the homology of the free loop space LM of an oriented manifold M. In this paper we show how to extend this construction to a topological conformal field theory of degree d. In…
We study homogeneity aspects of metric spaces in which all triples of distinct points admit pairwise different distances; such spaces are called isosceles-free. In particular, we characterize all homogeneous isosceles-free spaces up to…
In this paper we study the topology of the cobordism category of open and closed strings. This is a 2-category in which the objects are compact one-manifolds whose boundary components are labeled by an indexing set (the set of "D-branes"),…
For any resource theory it is essential to identify tasks for which resource objects offer advantage over free objects. We show that this identification can always be accomplished for resource theories of quantum measurements in which free…
We introduce a topology on the space of all isomorphism types represented in a given class of countable models, and use this topology as an aid in classifying the isomorphism types. This mixes ideas from effective descriptive set theory and…
A homomorphism from a completely metrizable topological group into a free product of groups whose image is not contained in a factor of the free product is shown to be continuous with respect to the discrete topology on the range. In…
We provide base change theorems, projection formulae and Verdier duality for both cohomology and homology in the context of finite topological spaces
For a field $\ef$, the discrete topological vector spaces over $\ \ef$ are essentially of the form $\ef^{\alpha}$ where $\alpha$ is an ordinal. With additional appropriate properties, they are isomorphic to $\ef^{(\beta)}$ where $\beta$ is…
The algebra of linear and quadratic functions of basic observables on the phase space of either the free particle or the harmonic oscillator possesses a finite-dimensional anomaly. The quantization of these systems outside the critical…
We show that in the category of preordered sets, there is a natural notion of pretorsion theory, in which the partially ordered sets are the torsion-free objects and the sets endowed with an equivalence relation are the torsion objects.…