MATH527_HW9 - Serge Ballif MATH 27 Homework 9 November 9,...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Serge Ballif MATH 27 Homework 9 November 9, 2007 Problem 1. Let p : E B be a covering map. Assume E is path connected and B is simply connected. Show that p is a homeomorphism. Since E is path connected, the lifting correspondence : 1 ( B,b ) p- 1 ( b ) is surjective. This is true for each b B . Since 1 ( B,b ) is trivial, we know that p- 1 ( b ) consists of just a single element. Thus, p is a bijection. Also, p is continuous as a covering map and p- 1 is continuous, because p is an open map. Thus, p is a homeomorphism. Problem 2. Let G be a group of homeomorphisms of X . The action of G on X is said to be fixed-point free if no element of G other than the identity e has a fixed point. Show that if X is Hausdorff, and if G is a finite group of homeomorphisms of X whose action is fixed-point free then the action of G is properly discontinuous. Recall that the action of G is properly discontinuous if for every x X , there exists a neighborhood U of x such that g (...
View Full Document

Page1 / 2

MATH527_HW9 - Serge Ballif MATH 27 Homework 9 November 9,...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online