Almost disjoint families and topology
... and continued in [34, 68, 92] and [4]. One of the basic problems of [88] was recently solved in [4] by consistently constructing a MAD family maximal in the Katětov order. This is an ongoing project with many fundamental problems open. Almost disjoint families are also one of the natural combinator ...
... and continued in [34, 68, 92] and [4]. One of the basic problems of [88] was recently solved in [4] by consistently constructing a MAD family maximal in the Katětov order. This is an ongoing project with many fundamental problems open. Almost disjoint families are also one of the natural combinator ...
Discrete Crossed product C*
... set of selfadjoint elements in A. All homomorphisms between C*-algebras are assumed to be ∗ -preserving, and ideals in C*-algebras are always closed and two-sided. Unless otherwise stated, a representation of a C*-algebra on a Hilbert space is presumed to be nondegenerate, and our Hilbert spaces are ...
... set of selfadjoint elements in A. All homomorphisms between C*-algebras are assumed to be ∗ -preserving, and ideals in C*-algebras are always closed and two-sided. Unless otherwise stated, a representation of a C*-algebra on a Hilbert space is presumed to be nondegenerate, and our Hilbert spaces are ...
STRONGLY ALMOST DISJOINT SETS AND WEAKLY UNIFORM
... (e) ⇒ (a). Assume τ = σ + , and let hPξ : ξ < λ+ i witness that Sp(σ, λ) holds. For each ξ let Rξ be the union of Pξ and the set of initial segments of elements of λ+ Pξ . Let S ξ ∈ Sτ \ {τ }. Now if x ⊂ ξ is any cofinal subset of ξ of order typeSτ , then x = ν∈σ xν , where the family of all initial ...
... (e) ⇒ (a). Assume τ = σ + , and let hPξ : ξ < λ+ i witness that Sp(σ, λ) holds. For each ξ let Rξ be the union of Pξ and the set of initial segments of elements of λ+ Pξ . Let S ξ ∈ Sτ \ {τ }. Now if x ⊂ ξ is any cofinal subset of ξ of order typeSτ , then x = ν∈σ xν , where the family of all initial ...
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.