E.7 Alaoglu`s Theorem
... call T . Since this is a smaller family of seminorms, we have T ⊆ σ(X ∗ , X). Suppose that µ ∈ X ∗ and ρxn (µ) = 0 for every n ∈ N. Then we have hxn , µi = 0 for every n. Since {xn }n∈N is dense in X and µ is continuous, this implies that µ = 0. Consequently, by Exercise E.17, the topology T is Haus ...
... call T . Since this is a smaller family of seminorms, we have T ⊆ σ(X ∗ , X). Suppose that µ ∈ X ∗ and ρxn (µ) = 0 for every n ∈ N. Then we have hxn , µi = 0 for every n. Since {xn }n∈N is dense in X and µ is continuous, this implies that µ = 0. Consequently, by Exercise E.17, the topology T is Haus ...
Houston Journal of Mathematics
... . ob vlous, since r and ra share the classes of dense subsets classes of sg-open subsets (see [l]). (4) + (1). Let x E Xi and suppose of intF, and without ...
... . ob vlous, since r and ra share the classes of dense subsets classes of sg-open subsets (see [l]). (4) + (1). Let x E Xi and suppose of intF, and without ...
Decompositions of normality and interrelation among its variants
... Continuing in this manner we obtain a collection V = {Vα : α ∈ Λ} of open sets which is a shrinking of U provided V covers X. Let x ∈ X, since V is a point finite open cover of X, x belongs to finitely many members of U, say Uα1 , Uα2 , . . . , Uαk . Suppose α = max{α1 , α2 , . . . , αk }. Now x ∈ / ...
... Continuing in this manner we obtain a collection V = {Vα : α ∈ Λ} of open sets which is a shrinking of U provided V covers X. Let x ∈ X, since V is a point finite open cover of X, x belongs to finitely many members of U, say Uα1 , Uα2 , . . . , Uαk . Suppose α = max{α1 , α2 , . . . , αk }. Now x ∈ / ...
Fuchsian Groups: Intro
... to G. We directly exhibit the homomorphism φ : G → C −1 GC given by φ : T 7→ C −1 T C, along with its inverse µ : V 7→ CV C −1 . If the conjugator is chosen from PSL(2, R), then it preserves distances in H and hence will also respect the topological properties of the group its applied to. In particu ...
... to G. We directly exhibit the homomorphism φ : G → C −1 GC given by φ : T 7→ C −1 T C, along with its inverse µ : V 7→ CV C −1 . If the conjugator is chosen from PSL(2, R), then it preserves distances in H and hence will also respect the topological properties of the group its applied to. In particu ...
5a.pdf
... M where two are equivalent if there is an isometry homotopic to the identity between them. In order to understand hyperbolic structures on a surface we will cut the surface up into simple pieces, analyze structures on these pieces, and study the ways they can be put together. Before doing this we ne ...
... M where two are equivalent if there is an isometry homotopic to the identity between them. In order to understand hyperbolic structures on a surface we will cut the surface up into simple pieces, analyze structures on these pieces, and study the ways they can be put together. Before doing this we ne ...