Global homeomorphisms between finite dimensional spaces

Abstract

It is well-known from covering space theory that global homeomorphism problem can be reduced to finding conditions for a local homeomorphism to satisfy the line lifting property. We will show that this property is equivalent to a limiting condition (which in many cases easy to verify) which we call by L. We will use this condition L to derive several results on global homeomorphisms due to Roy Plastock. We will prove an approximation theorem due to More and Rheinboldt and this result will then be used to prove Gale-Nikaido's theorem under weaker assumptions. In the last section we will prove a result due to McAuley for light open mappings. We will end this chapter with an old conjecture of Whyburn.