Vol. 15, No. 4, 1965

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 290: 1  2
Vol. 289: 1  2
Vol. 288: 1  2
Vol. 287: 1  2
Vol. 286: 1  2
Vol. 285: 1  2
Vol. 284: 1  2
Vol. 283: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Editorial Board
Officers
Special Issues
Submission Guidelines
Submission Form
Subscriptions
Contacts
Author Index
To Appear
 
ISSN: 0030-8730
Some topological properties of certain spaces of differentiable homeomorphisms of disks and spheres

Jack Max Robertson

Vol. 15 (1965), No. 4, 1383–1389
Abstract

Let Dn = {x En : |x|1}, and Sn = {x En+1 : |x| = 1}. We denote by Hn the space of C homeomorphisms of Dn onto itself leaving a neighborhood of the boundary fixed. Let Kn be the space of C orientation preserving homeomorphisms of Sn onto itself. It is not required that maps in the two spaces have differentiable inverses. In both space the Ck topology is used.

The purpose of this paper is to establish the following two theorems:

Theorem 1. Hn is contractible to a point for any n.

Theorem 2. Kn is arcwise connected for any n.

Mathematical Subject Classification
Primary: 54.80
Milestones
Received: 16 September 1964
Published: 1 December 1965
Authors
Jack Max Robertson