Regular Combinatorial Maps - People
... Ramified coverings have been studied by both Tits 1281 and Ronan [24, 251 in the more general setting of chamber systems. The concept of homotopy subsequently used in this paper was introduced by Tits. Numerous results on coverings of chamber systems, including a generalization of our Corollary 3.2, ...
... Ramified coverings have been studied by both Tits 1281 and Ronan [24, 251 in the more general setting of chamber systems. The concept of homotopy subsequently used in this paper was introduced by Tits. Numerous results on coverings of chamber systems, including a generalization of our Corollary 3.2, ...
Elementary Topology Problem Textbook O. Ya. Viro, O. A. Ivanov, N
... like a pure problem book. It would be easy to make the book looking like hundreds of other mathematical textbooks. For this purpose, it suffices to move all variations to the ends of their sections so that they would look like exercises to the basic text, and put the proofs of theorems immediately a ...
... like a pure problem book. It would be easy to make the book looking like hundreds of other mathematical textbooks. For this purpose, it suffices to move all variations to the ends of their sections so that they would look like exercises to the basic text, and put the proofs of theorems immediately a ...
HOPF ALGEBRAS AND QUADRATIC FORMS 1. Introduction Let Y
... when Y = Spec(R) and G = Spec(A), where A carries the natural structure of a finite and flat R-Hopf algebra. In this case the group scheme homomorphism ρ : G → O(q) may be viewed as endowing V with the structure of a module over the Hopf dual of A. Our goal is to understand the twist qX , constructe ...
... when Y = Spec(R) and G = Spec(A), where A carries the natural structure of a finite and flat R-Hopf algebra. In this case the group scheme homomorphism ρ : G → O(q) may be viewed as endowing V with the structure of a module over the Hopf dual of A. Our goal is to understand the twist qX , constructe ...
Grey subsets of Polish spaces
... For example, 0 A is open, i.e., upper semi-continuous (respectively, closed, i.e., lower semicontinuous) if and only if A is open (respectively, closed), 0 A v 0 B if and only if A ⊆ B, and so on. For grey sets, we have d A v X if and only if A v 0 X , and if Ai are all open (respectively, closed) t ...
... For example, 0 A is open, i.e., upper semi-continuous (respectively, closed, i.e., lower semicontinuous) if and only if A is open (respectively, closed), 0 A v 0 B if and only if A ⊆ B, and so on. For grey sets, we have d A v X if and only if A v 0 X , and if Ai are all open (respectively, closed) t ...
Covering space
In mathematics, more specifically algebraic topology, a covering map (also covering projection) is a continuous function p from a topological space, C, to a topological space, X, such that each point in X has an open neighbourhood evenly covered by p (as shown in the image); the precise definition is given below. In this case, C is called a covering space and X the base space of the covering projection. The definition implies that every covering map is a local homeomorphism.Covering spaces play an important role in homotopy theory, harmonic analysis, Riemannian geometry and differential topology. In Riemannian geometry for example, ramification is a generalization of the notion of covering maps. Covering spaces are also deeply intertwined with the study of homotopy groups and, in particular, the fundamental group. An important application comes from the result that, if X is a ""sufficiently good"" topological space, there is a bijection between the collection of all isomorphism classes of connected coverings of X and the conjugacy classes of subgroups of the fundamental group of X.