the topology of ultrafilters as subspaces of the cantor set and other
... First, we will observe that there are many (actually, as many as possible) nonhomeomorphic ultrafilters. However, the proof is based on a cardinality argument, hence it is not ‘honest’ in the sense of Van Douwen: it would be desirable to find ‘quotable’ topological properties that distinguish ultraf ...
... First, we will observe that there are many (actually, as many as possible) nonhomeomorphic ultrafilters. However, the proof is based on a cardinality argument, hence it is not ‘honest’ in the sense of Van Douwen: it would be desirable to find ‘quotable’ topological properties that distinguish ultraf ...
Sheaves of Modules
... In this chapter we work out basic notions of sheaves of modules. This in particular includes the case of abelian sheaves, since these may be viewed as sheaves of Zmodules. Basic references are [Ser55], [DG67] and [AGV71]. This is a chapter of the Stacks Project, version d9096d4, compiled on Oct 19, ...
... In this chapter we work out basic notions of sheaves of modules. This in particular includes the case of abelian sheaves, since these may be viewed as sheaves of Zmodules. Basic references are [Ser55], [DG67] and [AGV71]. This is a chapter of the Stacks Project, version d9096d4, compiled on Oct 19, ...
Free modal algebras: a coalgebraic perspective
... for constructing free modal and distributive modal algebras. Modal algebras are algebraic models of (classical) modal logic and distributive modal algebras are algebraic models of positive (negation-free) modal logic. We will show how to construct free algebras for a variety V equipped with an opera ...
... for constructing free modal and distributive modal algebras. Modal algebras are algebraic models of (classical) modal logic and distributive modal algebras are algebraic models of positive (negation-free) modal logic. We will show how to construct free algebras for a variety V equipped with an opera ...
Chapter 7 Duality
... We begin this chapter with some general results on duality in a tensor category, followed by some general results on duality in certain triangulated categories. We then give our main application, showing that the full sub-category DM(S)pr of DM(S), gotten by taking the pseudo-abelian hull of the sub ...
... We begin this chapter with some general results on duality in a tensor category, followed by some general results on duality in certain triangulated categories. We then give our main application, showing that the full sub-category DM(S)pr of DM(S), gotten by taking the pseudo-abelian hull of the sub ...
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.