Corpus ID: 236318330

On the topologies of the exponential

  title={On the topologies of the exponential},
  author={Anna Cepek and D. Lejay},
Factorization algebras have been defined using three different topologies on the Ran space. We study these three different topologies on the exponential, which is the union of the Ran space and the empty configuration, and show that an exponential property is satisfied in each case. As a consequence we describe the weak homotopy type of the exponential Exp(X) for each topology, in the case where X is not connected. We also study these exponentials as stratified spaces and show that the metric… Expand
1 Citations

Figures from this paper

Constructible hypersheaves via exit paths
The goal of this article is to extend a theorem of Lurie ShA(X) = Fun(ExitA(X),S) representing constructible sheaves with values in S, the∞-category of spaces, on a stratified space X with poset ofExpand


Higher enveloping algebras
We provide spectral Lie algebras with enveloping algebras over the operad of little $G$-framed $n$-dimensional disks for any choice of dimension $n$ and structure group $G$, and we describe theseExpand
Sequential unions of core-compact spaces commute with products
is a homeomorphism. By doing so, we shall sharpen a traditional tool used in the topology of CW-complexes: since their definition by Whitehead, one typical problem is to show that a product of twoExpand
On the topological product of paracompact spaces
A space 5 is denned by Jean Dieudonné to be paracompact provided every covering of 5 by open sets has a neighborhood-finite refinement which covers it. Dieudonné proves that every metric separableExpand
Local structures on stratified spaces
We develop a theory of conically smooth stratified spaces and their smooth moduli, including a notion of classifying maps for tangential structures. We characterize continuous space-valued sheaves onExpand
Chiral Koszul duality
We extend the theory of chiral and factorization algebras, developed for curves by Beilinson and Drinfeld (American Mathematical Society Colloquium Publications, 51. American Mathematical Society,Expand
Hyperspaces of finite subsets which are homeomorphic to ℵ0-dimensional linear metric spaces
Abstract We show that the hyperspace F (X) of all nonempty finite subsets of a metric space X, topologized by the Hausdorff metric, is homeomorphic to the ℵ0-dimensional linear metric space l2f ifExpand
On nonseparable reflexive Banach spaces
The purpose of this paper is to show that certain known results concerning separable spaces hold also for nonseparable reflexive Banach spaces. Our main result (Theorem 1) proves a special case of aExpand
Strict convexity and smoothness of normed spaces
1. Definitions and outline of results. This paper contains the first examples of normed spaces not isomorphic to strictly convex or smooth spaces. The table below shows the properties now known to beExpand
Strict convexity and smoothness of normed spaces
V. L. Klee [ I I ] 1 5 and M. M. Day [6] have considered various problems on strict convexity and smoothness of normed spaces. In his paper, Day [6] raised several questions. Two of these are theExpand
Embeddings from the point of view of immersion theory: Part II
Let M and N be smooth manifolds without boundary. Immersion theory suggests that an understanding of the space of smooth embeddings emb(M,N) should come from an analysis of the cofunctor V |-->Expand