Abstracts of Papers
... rings are Jaffard. Furthermore, we introduce a new invariant allowing us to compute the number of Jaffard domains between any given extension of integral domains A ⊆ B. We also give a new characterization of valuation domains and one-dimensional Prfer domains and provide many examples to illustrate ...
... rings are Jaffard. Furthermore, we introduce a new invariant allowing us to compute the number of Jaffard domains between any given extension of integral domains A ⊆ B. We also give a new characterization of valuation domains and one-dimensional Prfer domains and provide many examples to illustrate ...
Free full version - topo.auburn.edu
... Choquet and Stephenson [7, 15] (see [3, 6] for recent advances in this field). The following interesting generalization of minimality was recently introduced by Morris and Pestov [11]: Definition 1.1. A topological group (G, τ ) is said to be locally minimal if there exists a neighbourhood of the id ...
... Choquet and Stephenson [7, 15] (see [3, 6] for recent advances in this field). The following interesting generalization of minimality was recently introduced by Morris and Pestov [11]: Definition 1.1. A topological group (G, τ ) is said to be locally minimal if there exists a neighbourhood of the id ...
topological closure of translation invariant preorders
... linear spaces. This property is naturally motivated from an algebraic viewpoint. Indeed, in the theory of partially ordered groups, it is precisely this property that brings together the group and order structures that are imposed on a given set. From a more applied point of view, we note that trans ...
... linear spaces. This property is naturally motivated from an algebraic viewpoint. Indeed, in the theory of partially ordered groups, it is precisely this property that brings together the group and order structures that are imposed on a given set. From a more applied point of view, we note that trans ...
MAT327H1: Introduction to Topology
... the smallest closed set containing A . Proposition x ∈ Å if and only if there exists an open U such that x ∈ U ⊂ A . Proof: ( ⇒ ) x ∈ Å , take U = Å . ( ⇐ ) If x ∈ U ⊂ A , U open, then Å ∪U = Å is open and contained in A . So U ⊂ Å and x∈ Å . Proposition x ∈ A if and only if for all open U , ...
... the smallest closed set containing A . Proposition x ∈ Å if and only if there exists an open U such that x ∈ U ⊂ A . Proof: ( ⇒ ) x ∈ Å , take U = Å . ( ⇐ ) If x ∈ U ⊂ A , U open, then Å ∪U = Å is open and contained in A . So U ⊂ Å and x∈ Å . Proposition x ∈ A if and only if for all open U , ...
ON THE TOPOLOGY OF WEAKLY AND STRONGLY SEPARATED
... Here, the nerve N ({∆i }) of the covering {∆i }i∈I is defined as the simplicial complex on T the vertex set I such that a finite subset σ ⊂ I is a face of N ({∆i }) if and only if i∈σ ∆i 6= ∅. 2.2. Equivariant Tools. In the following, we let G be any group. A G-simplicial complex is a simplicial com ...
... Here, the nerve N ({∆i }) of the covering {∆i }i∈I is defined as the simplicial complex on T the vertex set I such that a finite subset σ ⊂ I is a face of N ({∆i }) if and only if i∈σ ∆i 6= ∅. 2.2. Equivariant Tools. In the following, we let G be any group. A G-simplicial complex is a simplicial com ...
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.