Related papers: The extended future cover of a sofic shift
We construct a sofic approximation of $\mathbb F_2\times\mathbb F_2$ that is not essentially a "branched cover" of a sofic approximation by homomorphisms. This answers a question of L. Bowen.
A multidimensional sofic shift is called countably covered if it has an SFT cover containing only countably many configurations. In contrast to the one-dimensional setting, not all countable sofic shifts are countably covered. We…
Covering-based rough set theory is an extension to classical rough set. The main purpose of this paper is to study covering rough sets from a topological point of view. The relationship among upper approximations based on topological spaces…
See hep-ph/0304045
We construct a canonical extension for strong proximity lattices in order to give an algebraic, point-free description of a finitary duality for stably compact spaces. In this setting not only morphisms, but also objects may have distinct…
The canonical formalism for expanding metrics scenarios is presented. Non-unitary time evolution implied by expanding geometry is described as a trajectory over unitarily inequivalent representations at different times of the canonical…
Following the observational evidence for cosmic acceleration which may exclude a possibility for the universe to recollapse to a second singularity, we review alternative scenarios of its future evolution. Although the de Sitter asymptotic…
We address the question of when a covering of the boundary of a surface can be extended to a covering of the surface (equivalently: when is there a branched cover with a prescribed monodromy). If such an extension is possible, when can the…
The aim of this article is to find appropriate definitions for shifts of finite type and sofic shifts in a general context of symbolic dynamics. We start showing that the classical definitions of shifts of finite type and sofic shifts, as…
Various characterizations are offered of injectivity of the canonical fundamental group homomorphism for a certain class of inverse limit spaces. One application characterizes the existence of a kind of generalized universal cover.
This is a short survey illustrating some of the essential aspects of the theory of canonical extensions. In addition some topological results about canonical extensions of lattices with additional operations in finitely generated varieties…
General topology of the universe is descibed. It is concluded that topology of the present universe is greater or stronger than the topology of the universe in the past and topology of the future universe will be stronger or greater than…
The connection between the theory of permutation orbifolds, covering surfaces and uniformization is investigated, and the higher genus partition functions of an arbitrary permutation orbifold are expressed in terms of those of the original…
The coeffective differential complex on a symplectic manifold is extended both in length and in scope, unifying the constructions of various other authors.
We establish a new extension result for twisted canonical forms defined on a hypersurface with simple normal crossings of a projective manifold. Some of the examples presented in the appendix are showing that the bounds we obtain for the…
Several variations on the definition of a Formal Topology exist in the literature. They differ on how they express convergence, the formal property corresponding to the fact that open subsets are closed under finite intersections. We…
The paradigmatic transition from a small finite universe to an infinite unbounded fractal cosmos is briefly put into historical context and discussed.
We discuss holomorphic extension across a boundary point in terms of sector property. The point is of infinite type and the sector is accordingly "cusped" at the vertex.
We develop a generalized covering space theory for a class of uniform spaces called coverable spaces. Coverable spaces include all geodesic metric spaces, connected and locally pathwise connected compact topological spaces, in particular…
Complete cosmic evolution is a popular model in cosmology. But the possibility of other different cosmic evolution model can not be negated. The nonsingular bouncing scenario models are now found in literature. This work is a representation…