Related papers: On Two Topologies that were suggested by Zeeman
We show how to use topological ideas, such as compactness, to establish orderability properties of infinite groups. A new application is to provide a left-ordering for the group of PL homeomorphisms of a connected surface with boundary…
The article is devoted to a structure of topological spaces related with topological quasigroups. Regular and complete spaces over topological quasigroups are studied. Separations and embeddings are also investigated for them. Their…
It is shown that the extended teleparallel gravitational theories, known as f(T) theories, inherit some on shell local Lorentz invariance associated with the tetrad field defining the spacetime structure. We discuss some enlightening…
The 2+1 dimensional lattice models of Levin and Wen [PRB 71, 045110 (2005)] provide the most general known microscopic construction of topological phases of matter. Based heavily on the mathematical structure of category theory, many of the…
A physical interpretation of the recently discovered vast class of vacuum space-times, which stably violate the strong cosmic censor conjecture (in its usual broad formulation) in four dimensions, is exhibited. Namely, by elementary Morse…
These expository notes are dedicated to the study of the topology of configuration spaces of manifolds. We give detailed computations of many invariants, including the fundamental group of the configuration spaces of $\mathbb{R}^2$, the…
Do the spacetime manifolds which feature in our best scientific theories reflect anything metaphysically weighty in the world (e.g., any fundamental substances or relations)? Should we extend our notions of space and time beyond the…
We extend the Stone duality between topological spaces and locales to include order: there is an adjunction between the category of preordered topological spaces satisfying the so-called open cone condition, and the newly defined category…
The order topology $\tau_o(P)$ (resp. the sequential order topology $\tau_{os}(P)$) on a poset $P$ is the topology that has as its closed sets those that contain the order limits of all their order convergent nets (resp. sequences). For a…
Study of symmetry, topology and geometric phase can reveal many new and interesting results on the topological states of matter. Here we present a completely new and interesting result of symmetry, topology and quantization of geometric…
We explore spacetime symmetries and topologies of the two metric sectors in Hassan-Rosen bimetric theory. We show that, in vacuum, the two sectors can either share or have separate spacetime symmetries. If stress-energy tensors are present,…
The strict globular $\omega$-categories formalize the execution paths of a parallel automaton and the homotopies between them. One associates to such (and any) $\omega$-category $\C$ three homology theories. The first one is called the…
In this paper we put forward the definition of particular subsets on a unital C*-algebra, that we call isocones, and which reduce in the commutative case to the set of continuous non-decreasing functions with real values for a partial order…
Classical mechanics, relativity, electrodynamics and quantum mechanics are often depicted as separate realms of physics, each with its own formalism and notion. This remains unsatisfactory with respect to the unity of nature and to the…
We develop a new class of clockwork theories with an augmented structure of the near-neighbour interactions along a one-dimensional closed chain. Such a topology leads to new and attractive features in addition to generating light states…
We theoretically demonstrate that the second-order topological insulator with robust corner states can be realized in two-dimensional $\mathbb{Z}_2$ topological insulators by applying an in-plane Zeeman field. Zeeman field breaks the…
The necessity of a theory of General Topology and, most of all, of Algebraic Topology on locally finite metric spaces comes from many areas of research in both Applied and Pure Mathematics: Molecular Biology, Mathematical Chemistry,…
In this article we study two "strong" topologies for spaces of smooth functions from a finite-dimensional manifold to a (possibly infinite-dimensional) manifold modeled on a locally convex space. Namely, we construct Whitney type topologies…
Any two infinite-dimensional (separable) Hilbert spaces are unitarily isomorphic. The sets of all their self-adjoint operators are also therefore unitarily equivalent. Thus if all self-adjoint operators can be observed, and if there is no…
One of the prime motivation for topology was Homotopy theory, which captures the general idea of a continuous transformation between two entities, which may be spaces or maps. In later decades, an algebraic formulation of topology was…