Material Information 

Title: 
Topological means 

Physical Description: 
v, 41 leaves. : ; 28 cm. 

Language: 
English 

Creator: 
Crummer, Arthur, 1943 ( Dissertant ) Bacon, Philip ( Thesis advisor ) Wallace, A. D. ( Reviewer ) Keesling, James ( Reviewer ) Sigmon, Kermit ( Reviewer ) Irey, Richard ( Reviewer ) 

Publisher: 
University of Florida 

Place of Publication: 
Gainesville, Fla. 

Publication Date: 
1971 

Copyright Date: 
1971 
Subjects 

Subjects / Keywords: 
Algebraic topology ( lcsh ) Mathematics thesis Ph. D Dissertations, Academic  Mathematics  UF 

Genre: 
bibliography ( marcgt ) nonfiction ( marcgt ) theses ( marcgt ) 
Notes 

Abstract: 
then X is said to admit an nmean provided there is a continuous
function m : X » X such that m(x,. . . ,x) = x for each element x of
X and such that m(x., , ... ,x ) is invariant under permutations of
1 n
x x . In Section 1, a summary of known results is given. In
Section 2, we define what is called a uniform nmean, show, that a space
admits a uniform 2mean if and only if it admits a 2mean and that if
a space admits a uniform nmean (n^3), then it admits an nmean.
It is proved that if a compact Hausdorff space is a retract of its
hyperspace, then it is acyclic.
In Section 3, we characterize those solenoids which admit an
nmean (Proposition 3.5), give an example of a nonacyclic continuum
which admits an nmean for each positive integer n, and show that the
admissibility of an nmean is a strictly weaker condition than admissibility
of a uniform nmean whenever n>2.
In Section 4, it is shown that the first Alexander cohomology
group of any space is torsion free (integral coefficients) and this is used to prove a technical result (Proposition 4.7) which is used for
several purposes: we are able to give new examples of contractible
spaces which admit no nmeans , to prove that if a compact Hausdorff
space admits an nmean (n^2), then each of its nonzero cohomology
groups (integral coefficients) is uniquely ndivisible, and to prove
that if a continuum X admits an idempotent continuous multiplication
having a zero, then X is acyclic.
Section 5 contains a few open questions. 

Thesis: 
Thesis  University of Florida. 

Bibliography: 
Bibliography: leaves 3940. 

General Note: 
Manuscript copy. 

General Note: 
Vita. 
Record Information 

Bibliographic ID: 
UF00097662 

Volume ID: 
VID00001 

Source Institution: 
University of Florida 

Holding Location: 
University of Florida 

Rights Management: 
All rights reserved by the source institution and holding location. 

Resource Identifier: 
alephbibnum  000570666 oclc  13717680 notis  ACZ7645 
