A non-weakly amenable augementation ideal
... are primarily concerned with the counterexample just mentioned, we will not be working in anything like the generality we have described above. Many results will be for the case in which G and X are discrete. Some measure theoretic complications occur in the continuous case and we get our counterexa ...
... are primarily concerned with the counterexample just mentioned, we will not be working in anything like the generality we have described above. Many results will be for the case in which G and X are discrete. Some measure theoretic complications occur in the continuous case and we get our counterexa ...
Reduced coproducts of compact Hausdorff spaces
... We will adopt this as our definition of the topological reduced coproduct; the reader will no doubt observe that this definition makes sense when applied to any family of Tichonov spaces. The result is always compact Hausdorff (and is in fact Boolean whenever the factors are strongly 0-dimensional). ...
... We will adopt this as our definition of the topological reduced coproduct; the reader will no doubt observe that this definition makes sense when applied to any family of Tichonov spaces. The result is always compact Hausdorff (and is in fact Boolean whenever the factors are strongly 0-dimensional). ...
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.