Metric geometry of locally compact groups
... of his articles [Grom–81b, Grom–84, Grom–87, Grom–93], the group community has been used to consider a group (with appropriate conditions) as a metric space, and to concentrate on large-scale properties of such metric spaces. Different classes of groups can be characterized by the existence of metric ...
... of his articles [Grom–81b, Grom–84, Grom–87, Grom–93], the group community has been used to consider a group (with appropriate conditions) as a metric space, and to concentrate on large-scale properties of such metric spaces. Different classes of groups can be characterized by the existence of metric ...
A geometric introduction to K-theory
... 1. Algebraic intersection multiplicities Let Z be the parabola y = x2 in R2 , and let W be the tangent line at the vertex: the line y = 0. Then Z and W have an isolated point of intersection at (0, 0). Since high school you have known how to associate a multiplicity with this intersection: it is mul ...
... 1. Algebraic intersection multiplicities Let Z be the parabola y = x2 in R2 , and let W be the tangent line at the vertex: the line y = 0. Then Z and W have an isolated point of intersection at (0, 0). Since high school you have known how to associate a multiplicity with this intersection: it is mul ...
Peterzil
... (8) Assume that X is a definably connected subset of M n and f : X → M is definable and continuous. Show that graph(f ) is definably connected. (9) Let {Xa : a ∈ M n } be a uniformly definable family of subsets of M k . Show that the set {a ∈ M n : Xa is finite } is definable (this should be done ju ...
... (8) Assume that X is a definably connected subset of M n and f : X → M is definable and continuous. Show that graph(f ) is definably connected. (9) Let {Xa : a ∈ M n } be a uniformly definable family of subsets of M k . Show that the set {a ∈ M n : Xa is finite } is definable (this should be done ju ...
Proper Morphisms, Completions, and the Grothendieck Existence
... in §1.1 with the following technical result: if X is a quasi-compact separated spectral algebraic space, then X admits a scallop decomposition (in the sense of Definition VIII.2.5.5). As a consequence, we will see that for any quasi-compact strongly separated morphism f : X → Y, there is a well-beha ...
... in §1.1 with the following technical result: if X is a quasi-compact separated spectral algebraic space, then X admits a scallop decomposition (in the sense of Definition VIII.2.5.5). As a consequence, we will see that for any quasi-compact strongly separated morphism f : X → Y, there is a well-beha ...
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... b-closedness in terms of supra b-open set and supra b-closed set, respectively. Now, we introduce the concept of supra pre-open sets and study some basic properties of it. Also, we introduce the concepts of supra pre-continuous maps, supra pre-open maps and supra pre-closed maps and investigate seve ...
... b-closedness in terms of supra b-open set and supra b-closed set, respectively. Now, we introduce the concept of supra pre-open sets and study some basic properties of it. Also, we introduce the concepts of supra pre-continuous maps, supra pre-open maps and supra pre-closed maps and investigate seve ...