In this paper, we first present a new type of the concept of open sets by expressing some properties of arbitrary mappings on a power set. With the generalization of the closure spaces in categorical topology, we introduce the generalized topological spaces and the concept of generalized continuity and become familiar with weak and strong structures for generalized topological spaces. Then, int...

The Universe Type System is an ownership type system for object-oriented programming languages that hierarchically structures the object store; it is used to reason modularly about programs. We formalise Universe Types for a core subset of Java in two steps: We first define a Topological Type System that structures the object store hierarchically into an ownership tree, and demonstrate soundnes...

The topological complexity TC(X) is a numerical homotopy invariant of a topological space X which is motivated by robotics and is similar in spirit to the classical Lusternik–Schnirelmann category of X. Given a mechanical system with configuration space X, the invariant TC(X) measures the complexity of all possible motion planning algorithms designed for the system. In this paper, we compute th...

In a previous paper the authors developed an operator-algebraic approach to Lewis Bowen’s sofic measure entropy that yields invariants for actions of countable sofic groups by homeomorphisms on a compact metrizable space and by measure-preserving transformations on a standard probability space. We show here that these measure and topological entropy invariants both coincide with their classical...

This paper presents how to design and implement a simple mass/spring system on a general-purpose topological structure. This way, topological inquiries or changes can be handled robustly so that the mesh remains consistent and a manifold.

The topology of a topological material can be encoded in its surface states. These surface states can only be removed by a bulk topological quantum phase transition into a trivial phase. Here we use photoemission spectroscopy to image the formation of protected surface states in a topological insulator as we chemically tune the system through a topological transition. Surprisingly, we discover ...

Topological Kondo insulators have been proposed as a new class of topological insulators in which non-trivial surface states reside in the bulk Kondo band gap at low temperature due to strong spin-orbit coupling. In contrast to other three-dimensional topological insulators, a topological Kondo insulator is truly bulk insulating. Furthermore, strong electron correlations are present in the syst...

In this article we study two different generalizations of von Neumann regularity, namely strong topological regularity and weak regularity, in the Banach algebra context. We show that both are hereditary properties and under certain assumptions, weak regularity implies strong topological regularity. Then we consider strong topological regularity of certain concrete algebras. Moreover we obtain ...

We characterize positive topological entropy for quasi-state space homeomorphisms induced from C∗-algebra automorphisms in terms of dynamically generated subspaces isomorphic to l1. This geometric condition is also used to give a description of the topological Pinsker algebra. In particular we obtain a geometric characterization of positive entropy for topological dynamical systems, as well as ...

We study the bifurcation diagram of the Rössler system. It displays the various dynamical regimes of the system (stable or chaotic) when a parameter is varied. We choose a diagram that exhibits coexisting attractors and banded chaos. We use the topological characterization method to study these attractors. Then, we detail how the templates of these attractors are subtemplates of a unique templa...