Title: Topological means
Full Citation
Permanent Link: http://ufdc.ufl.edu/UF00097662/00001
 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 / Keywords: Algebraic topology   ( lcsh )
Mathematics thesis Ph. D
Dissertations, Academic -- Mathematics -- UF
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
theses   ( marcgt )
Abstract: then X is said to admit an n-mean 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 n-mean, show, that a space admits a uniform 2-mean if and only if it admits a 2-mean and that if a space admits a uniform n-mean (n^3), then it admits an n-mean. 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 n-mean (Proposition 3.5), give an example of a non-acyclic continuum which admits an n-mean for each positive integer n, and show that the admissibility of an n-mean is a strictly weaker condition than admissibility of a uniform n-mean 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 n-means , to prove that if a compact Hausdorff space admits an n-mean (n^2), then each of its non-zero cohomology groups (integral coefficients) is uniquely n-divisible, 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 39-40.
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


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