New chaotic planar attractors from smooth zero entropy interval maps
... homeomorphism of R must fix a point in an invariant plane nonseparating compact and connected set (continuum). The original work of Cartwright and Littlewood, motivated by problems in differential equations, in which they were led to consider invariant sets whose frontiers were indecomposable, brough ...
... homeomorphism of R must fix a point in an invariant plane nonseparating compact and connected set (continuum). The original work of Cartwright and Littlewood, motivated by problems in differential equations, in which they were led to consider invariant sets whose frontiers were indecomposable, brough ...
Open set of eigenvalues and SVEP
... in X, a contradiction. Therefore T has SVEP. Note that the operator M from the above proof is decomposable. Therefore T has the decomposition property (δ), which means that T is in a some sense close to the class of decomposable operators. However, it is probably not decomposable. It is for sure not ...
... in X, a contradiction. Therefore T has SVEP. Note that the operator M from the above proof is decomposable. Therefore T has the decomposition property (δ), which means that T is in a some sense close to the class of decomposable operators. However, it is probably not decomposable. It is for sure not ...
Chapter 2: Manifolds
... Then any element of the group can be written as g(a) where a = (a1 , · · · , an ) . Since the composition of two elements of G must be another element of G, we can write g(a)g(b) = g(φ(a, b)) where φ = (φ1 , · · · , φn ) are n functions of a and b. Then for a Lie group, the functions φ are smooth (r ...
... Then any element of the group can be written as g(a) where a = (a1 , · · · , an ) . Since the composition of two elements of G must be another element of G, we can write g(a)g(b) = g(φ(a, b)) where φ = (φ1 , · · · , φn ) are n functions of a and b. Then for a Lie group, the functions φ are smooth (r ...
18. Fibre products of schemes The main result of this section is
... the most trivial examples) and it turns out that there is an appropriate condition for schemes (and in fact morphisms of schemes) which is a replacement for the Hausdorff condition for topological spaces. Finally we turn to the problem of glueing morphisms, which is the ...
... the most trivial examples) and it turns out that there is an appropriate condition for schemes (and in fact morphisms of schemes) which is a replacement for the Hausdorff condition for topological spaces. Finally we turn to the problem of glueing morphisms, which is the ...
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.