Open Covers and Symmetric Operators
... refinement of A if for every B ∈ B there exists a A ∈ A such that B ⊂ A. The family B is said to be a precise refinement of A if B and A are indexed by the same index set S and for every s ∈ S Bs ⊂ As . 2.2 Definition. Let A = {As : s ∈ S} be a subfamily of P(X). The star of a set Y ⊂ X with respect ...
... refinement of A if for every B ∈ B there exists a A ∈ A such that B ⊂ A. The family B is said to be a precise refinement of A if B and A are indexed by the same index set S and for every s ∈ S Bs ⊂ As . 2.2 Definition. Let A = {As : s ∈ S} be a subfamily of P(X). The star of a set Y ⊂ X with respect ...
Non-commutative Donaldson--Thomas theory and vertex operators
... one of A –modules by a derived equivalence. A parameter gives a Bridgeland’s stability condition of this derived category, and hence a core A of a t-structure on it (Definition 1.7). In fact, we have two specific parameters such that the corresponding t-structures coincide with the ones given by ...
... one of A –modules by a derived equivalence. A parameter gives a Bridgeland’s stability condition of this derived category, and hence a core A of a t-structure on it (Definition 1.7). In fact, we have two specific parameters such that the corresponding t-structures coincide with the ones given by ...
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.