From Wikipedia, the free encyclopedia
In
algebraic topology , a mean or mean operation on a
topological space X is a
continuous ,
commutative ,
idempotent
binary operation on X . If the operation is also
associative , it defines a
semilattice . A classic problem is to determine which spaces admit a mean. For example,
Euclidean spaces admit a mean -- the usual
average of two vectors -- but
spheres of positive dimension do not, including the
circle .
Further reading
Aumann, G. (1943),
"Über Räume mit Mittelbildungen." , Mathematische Annalen , 119 (2): 210–215,
doi :
10.1007/bf01563741 .
Sobolewski, Mirosław (2008), "Means on chainable continua",
Proceedings of the American Mathematical Society , 136 (10): 3701–3707,
doi :
10.1090/s0002-9939-08-09414-8 .
T. Banakh, W. Kubis, R. Bonnet (2014),
"Means on scattered compacta" , Topological Algebra and Its Applications , 2 (1),
arXiv :
1309.2401 ,
doi :
10.2478/taa-2014-0002 {{
citation }}
: CS1 maint: multiple names: authors list (
link ) .
Charatonik, Janusz J. (2003),
"Selected problems in continuum theory" (PDF) , Proceedings of the Spring Topology and Dynamical Systems Conference, Topology Proceedings , 27 (1): 51–78,
MR
2048922 .