Related papers: Chain Recurrence For General Spaces
The article introduces the concept of uniformity, which is formulated as a scheme of axioms. The connection of this concept with ordered sets is studied. The effectiveness of using axiom schemes as a convenient and short way of replacing…
The work is motivated by the papers [Ba1], [Ba2], [Ba7], [Ba11], [Be] and [Be-Tu]. In particular, the strong homology groups of continuous maps were defined and studied in [Be] and [Be-Tu]. To show that given groups are homology type…
Calculi of string diagrams are increasingly used to present the syntax and algebraic structure of various families of circuits, including signal flow graphs, electrical circuits and quantum processes. In many such approaches, the semantic…
As shown by the development of Special Relativity the simultaneity concept should be related to that of reference frame. Poincare' proposed to define the simultaneity of two events by means of light signals following what is nowadays known…
General relativity can be recast as a theory of connections by performing a canonical transformation on its phase space. In this form, its (kinematical) structure is closely related to that of Yang-Mills theory and topological field…
We prove some extension theorems involving uniformly continuous maps of the universal Urysohn space. We also prove reconstruction theorems for certain groups of autohomeomorphisms of this space and of its open subsets.
We provide a formal, simple and intuitive theory of rational decision making including sequential decisions that affect the environment. The theory has a geometric flavor, which makes the arguments easy to visualize and understand. Our…
Graph invariants provide a powerful analytical tool for investigation of abstract structures of graphs. They, combined in convenient relations, carry global and general information about a graph and its various substructures such as cycle…
It is shown that certain lower semi-continuous maps from a paracompact space to the family of closed subsets of the bundle space of a Banach bundle admit continuous selections. This generalization of the theorem of Douady, dal…
We study the relation of $L$-equivalence, which derives from the construction of the free locally convex spaces, through a concept that particularizes several notions related to the simultaneous extension of continuous functions. We also…
Projective spaces for finite-dimensional vector spaces over general fields are considered. The geometry of these spaces and the theory of line bundles over these spaces is presented. Particularly, the space of global regular sections of…
In this paper, we consider certain topological properties along with certain types of mappings on these spaces defined by the notion of ideal convergence. In order to do that, we primarily follow in the footsteps of the earlier studies of…
General relativity and quantum mechanism are two separate rules of modern physics explaining how nature works. Both theories are accurate, but the direct connection between two theories was not yet clarified. Recently, researchers blur the…
Complex network theory has been applied to solving practical problems from different domains. In this paper, we present a general framework for complex network applications. The keys of a successful application are a thorough understanding…
We consider general structures where formulas have truth values in the real unit interval as in continuous model theory, but whose predicates and functions need not be uniformly continuous with respect to a distance predicate. Every general…
Both the path integral measure in field theory and ensembles of neural networks describe distributions over functions. When the central limit theorem can be applied in the infinite-width (infinite-$N$) limit, the ensemble of networks…
The paper introduces the class of O-metric spaces, a novel generalization of metric-type spaces, classifying almost all possible metric types into upward and downward O-metrics. We list some topologies arising from O-metrics and discuss…
This paper establishes the equivalence of the Aubin property and the strong regularity for generalized equations over $C^2$-cone reducible sets. This result resolves a long-standing question in variational analysis and extends the…
Understanding realistic complex systems requires confronting significant conceptual, theoretical and experimental limitations rooted in the persistence of views that originated in the mechanics of simple moving bodies. We define the…
The concept of b-linear functional and its different types of continuity in linear n-normed space are presented and some of their properties are being established. We derive the Uniform Boundedness Principle and Hahn-Banach extension…