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

Subject Categories:

  • Theoretical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE