![arXiv:1311.6308v2 [math.AG] 27 May 2016](http://s1.studyres.com/store/data/014155230_1-8dc9a9d84bdbfdfdd374aa0278f9f3e1-300x300.png)
1 Comparing cartesian closed categories of (core) compactly
... A topology on C(X, Y ) is said to be exponential if continuity of a function f : A×X → Y is equivalent to that of its transpose f : A → C(X, Y ). When an exponential topology exists, it is unique, and we denote the resulting space by [X ⇒ Y ]. This is elaborated in Section 2 below. In this case, tra ...
... A topology on C(X, Y ) is said to be exponential if continuity of a function f : A×X → Y is equivalent to that of its transpose f : A → C(X, Y ). When an exponential topology exists, it is unique, and we denote the resulting space by [X ⇒ Y ]. This is elaborated in Section 2 below. In this case, tra ...
Pants decompositions of random surfaces
... (To define a “random” hyperbolic surface we need a probability measure on the moduli space of hyperbolic metrics. We use the renormalized Weil-Petersson volume form. We discuss this notion of randomness more below.) As another piece of context for our result, we mention the analogous questions for h ...
... (To define a “random” hyperbolic surface we need a probability measure on the moduli space of hyperbolic metrics. We use the renormalized Weil-Petersson volume form. We discuss this notion of randomness more below.) As another piece of context for our result, we mention the analogous questions for h ...
INTRODUCTION TO ALGEBRAIC TOPOLOGY 1.1. Topological
... maps. Explicitly HomTop (X, Y ) is the set of continuous maps from X to Y and composition is a set map ◦ : HomTop (Y, Z) × HomTop (X, Y ) → HomTop (X, Z). These satisfy the Axioms of a category: the existence and properties of identity morphisms IdX ∈ HomTop (X, X) and associativity of composition o ...
... maps. Explicitly HomTop (X, Y ) is the set of continuous maps from X to Y and composition is a set map ◦ : HomTop (Y, Z) × HomTop (X, Y ) → HomTop (X, Z). These satisfy the Axioms of a category: the existence and properties of identity morphisms IdX ∈ HomTop (X, X) and associativity of composition o ...
- Free Documents
... networks can be characterized as simages of a metric space M under a coveringmap f, and many results have been proved , , , . Recently, some authors have tried to generalize these results , , . In , Y. Ge and J. Shen have obtained the following. Theorem .. , Theorem . Let f, M, X, P be a Ponomarevsy ...
... networks can be characterized as simages of a metric space M under a coveringmap f, and many results have been proved , , , . Recently, some authors have tried to generalize these results , , . In , Y. Ge and J. Shen have obtained the following. Theorem .. , Theorem . Let f, M, X, P be a Ponomarevsy ...
Fibrewise Compactly
... the closure Xwr\N of N in Xw is fibrewise compact over W. By shrinking W9 if necessary, we can arrange for 7 to admit a section t over W such that t(b) = y. Then H meets (XwnN) xwtW in a closed set, since (Xwr\N) xwtW is fibrewise compact over W. Since the intersection is closed in Xw xwtW it follow ...
... the closure Xwr\N of N in Xw is fibrewise compact over W. By shrinking W9 if necessary, we can arrange for 7 to admit a section t over W such that t(b) = y. Then H meets (XwnN) xwtW in a closed set, since (Xwr\N) xwtW is fibrewise compact over W. Since the intersection is closed in Xw xwtW it follow ...
3-manifold
In mathematics, a 3-manifold is a space that locally looks like Euclidean 3-dimensional space. Intuitively, a 3-manifold can be thought of as a possible shape of the universe. Just like a sphere looks like a plane to a small enough observer, all 3-manifolds look like our universe does to a small enough observer. This is made more precise in the definition below.