Related papers: Inexistence of Zeeman's fine topology
We work on the family of topologies for the Minkowski manifold M. We partially order this family by inclusion to form the lattice \Sigma(M), and focus on the sublattice Z of topologies that induce the Euclidean metric space on every time…
The class of Zeeman topologies on spacetimes in the frame of relativity theory is considered to be of powerful intuitive justification, satisfying a sequence of properties with physical meaning, such as the group of homeomorphisms under…
E. C. Zeeman [1] has criticized the fact that in all articles and books until that moment (1967) the topology employed to work with the Minkowski space was the Euclidean one. He has proposed a new topology, which was generalized for more…
In this article we first observe that the Path topology of Hawking, King and MacCarthy is an analogue, in curved spacetimes, of a topology that was suggested by Zeeman as an alternative topology to his so-called Fine topology in Minkowski…
A constructive and straightforward proof of the existence of the Zeeman topology is provided, contradicting a fallacious claim contained in the paper "Does Zeeman's Fine Topology Exist?" available at arXiv:1003.3703v1.
The order horismos induces the Zeeman $Z$ topology, which is coarser than the Fine Zeeman Topology $F$. The causal curves in a spacetime under $Z$ are piecewise null. $F$ is considered to be the most physical topology in a spacetime…
We discuss the topological nature of the boundary spacetime, the conformal infinity of the ambient cosmological metric. Due to the existence of a homothetic group, the bounding spacetime must be equipped not with the usual Euclidean metric…
We prove that there does not exist global-in-time axisymmetric solutions to the time-like minimal submanifold system in Minkowski space. We further analyze the limiting geometry as the maximal time of existence is approached.
We report two theoretical discoveries for $\mathbb{Z}_2$-topological metals and semimetals. It is shown first that any dimensional $\mathbb{Z}_2$ Fermi surface is topologically equivalent to a Fermi point. Then the famous conventional no-go…
Estimation algebras have been extensively studied in Euclidean space, where finite-dimensional estimation algebras form the foundation of the Kalman and Benes filters, and have contributed to the discovery of many other finite-dimensional…
The group of homothetic symmetries in the conformal infinity (the $4$-dimensional "ambient boundary") of a $5$-dimensional spacetime restricts the choice of topology to a topology under which the group of homeomorphisms of a spacetime…
In a 1967 paper, Zeeman proposed a new topology for Minkowski spacetime, physically motivated but much more complicated than the standard one. Here a detailed study is given of some properties of the Zeeman topology which had not been…
We study extensions of Wermer's maximality theorem to several complex variables. We exhibit various smoothly embedded manifolds in complex Euclidean space whose hulls are non-trivial but contain no analytic disks. We answer a question posed…
Let $\otimes$ be the map which classifies the tensor product of two line bundles, an extension of this map to the space of all codimension 1 algebraic cycles is constructed. It is proved that this extension cannot exist in codimension…
It is consistent with ZF set theory that the Euclidean topology on the real line is not sequential, yet every infinite set of reals contains a countably infinite subset. This answers a question of Gutierres.
In the Letter, Xu et al. reported that edge modes disappear in the expanded structure of Wu-Hu model characterized by $\mathbb{Z}_2$ topological index, while appear in the trivial shrunken structure, when the edge cuts through the hexagonal…
Scalars and fermions can arise as Goldstone modes of non-linearly realised extensions of the Poincare group (with important implications for the soft limits of such theories): the Dirac-Born-Infeld scalar realises a higher-dimensional…
In this note we prove a nonexistence result for proper biharmonic maps from complete non-compact Riemannian manifolds of dimension \(m=\dim M\geq 3\) with infinite volume that admit an Euclidean type Sobolev inequality into general…
We study the existence of Riemannian metrics with zero topological entropy on a closed manifold M with infinite fundamental group. We show that such a metric does not exist if there is a finite simply connected CW complex which maps to M in…
$n$-scales are a generalization of time-scales that has been put forward to unify continuous and discrete analyses in higher dimensions. In this paper we investigate massive scalar field theory on a regular $n$-Scale. We have given the…