Modern descriptive set theory
... by a collection Ogen of sets that we want to declare to be open. Just let O to be the closure of the set Ogen on finite intersections and arbitrary unions. The category of topological spaces comes equipped with continuous functions and homeomorphisms. A map f : X → Y is continuous if preimages of op ...
... by a collection Ogen of sets that we want to declare to be open. Just let O to be the closure of the set Ogen on finite intersections and arbitrary unions. The category of topological spaces comes equipped with continuous functions and homeomorphisms. A map f : X → Y is continuous if preimages of op ...
Étale groupoids and their morphisms
... Boolean right normal bands: going to points B — Boolean right normal band. Let γ : B → B/D be the canonical morphism. Let G be an ultrafilter of B. There is a unique ultrafilter F of B/D such that γ(G ) = F and for some (equiv. for any) a ∈ G G = Ga,F = {b ∈ B : b eF a} = {b ∈ B : there is c ∈ B wi ...
... Boolean right normal bands: going to points B — Boolean right normal band. Let γ : B → B/D be the canonical morphism. Let G be an ultrafilter of B. There is a unique ultrafilter F of B/D such that γ(G ) = F and for some (equiv. for any) a ∈ G G = Ga,F = {b ∈ B : b eF a} = {b ∈ B : there is c ∈ B wi ...
separability of metric spaces - American Mathematical Society
... the 3-dimensional Euclidean space, on its removed edge, and the sequence of rectangles, congruent and parallel to the first one but lowered by 3 units, converging to the first one. C. Now repeat the process, using each of the rectangles in the sequence of rectangles as the first rectangle and for it ...
... the 3-dimensional Euclidean space, on its removed edge, and the sequence of rectangles, congruent and parallel to the first one but lowered by 3 units, converging to the first one. C. Now repeat the process, using each of the rectangles in the sequence of rectangles as the first rectangle and for it ...
1. Introduction - Departamento de Matemática
... between this “new” class of second countable spaces, and the classes of separable, Lindelöf spaces. In the literature it may be found a discussion of the equivalence, in ZF, of different ways of defining some well known topological notions. As interesting examples of this kind of study, we have tha ...
... between this “new” class of second countable spaces, and the classes of separable, Lindelöf spaces. In the literature it may be found a discussion of the equivalence, in ZF, of different ways of defining some well known topological notions. As interesting examples of this kind of study, we have tha ...
Scott Topology and its Relation to the Alexandroff Topology
... Scott open sets forms a topology called the Scott topology. Also, it shows that the Scott topology is sober over an algebraic dcpo. The base of the Scott topology is given by means of the set of all compact elements. The second compares between the Scott topology and the Alexandroff topology on fini ...
... Scott open sets forms a topology called the Scott topology. Also, it shows that the Scott topology is sober over an algebraic dcpo. The base of the Scott topology is given by means of the set of all compact elements. The second compares between the Scott topology and the Alexandroff topology on fini ...
NEARLY COUNTABLE DENSE HOMOGENEOUS SPACES 1
... countable dense sets. Then X contains a closed and scattered subset S of finite CantorBendixson rank which is closed under all homeomorphisms of X and has the property that X \ S is CDH. If X has at most n types of countable dense sets for some n ∈ N, then |S| ≤ n−1. The pseudoarc P is an example of ...
... countable dense sets. Then X contains a closed and scattered subset S of finite CantorBendixson rank which is closed under all homeomorphisms of X and has the property that X \ S is CDH. If X has at most n types of countable dense sets for some n ∈ N, then |S| ≤ n−1. The pseudoarc P is an example of ...