# Accession Number:

## AD0722363

# Title:

## The Monotone Mapping Problem,

# Descriptive Note:

# Corporate Author:

## WISCONSIN UNIV MADISON

# Personal Author(s):

# Report Date:

## 1971-04-01

# Pagination or Media Count:

## 30.0

# Abstract:

It is shown that for m 3,4,... there is a monotone map of Euclidean n space E sup n onto itself that is not compact. This completes the monotone mapping theorem posed by G. T. Whyburn. A key lemma in the treatment shows that there is a monotone map of a cube I sup 2 onto itself such that each point inverse intersects a base I sup 2 of I sup 3. If f is a map of I sup 3 onto I sup 3 which is a homeomorphism on Int I sup 3 and takes I sup 2 homeomorphically into I sup 2, one calls f Int I sup 2 joined to Int I sup 3 a drainage system for I sup 3. It is shown that there is a drainage system f Int I sup 2 joined to Int I sup 3 for I sup 3 and a monotone map g of I sup 3 - f Int I sup 2 joined to Int I sup 3 onto I sup 3 such that g is the identity on Bd I sup 3 - Int I sup 2. Author

# Descriptors:

# Subject Categories:

- Theoretical Mathematics