mean operation
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
- {{citation
| last = Aumann | first = G.
| journal = Mathematische Annalen
| pages = 210–215
| title = Über Räume mit Mittelbildungen.
| url = http://eudml.org/doc/160126
| volume = 119
| issue = 2
| year = 1943
| doi=10.1007/bf01563741 | doi-access = free}}.
- {{citation
| last = Sobolewski | first = Mirosław
| doi = 10.1090/s0002-9939-08-09414-8
| issue = 10
| journal = Proceedings of the American Mathematical Society
| pages = 3701–3707
| title = Means on chainable continua
| volume = 136
| year = 2008| doi-access = free
}}.
- {{citation
| last = T. Banakh | first = W. Kubis, R. Bonnet
| issue = 1
| journal = Topological Algebra and Its Applications
| title = Means on scattered compacta
| url = http://eudml.org/doc/266591
| volume = 2
| year = 2014| doi = 10.2478/taa-2014-0002 | doi-access = free
| arxiv = 1309.2401
}}.
- {{citation
| last = Charatonik | first = Janusz J.
| title = Selected problems in continuum theory
| url = http://topology.nipissingu.ca/tp/reprints/v27/tp27107.pdf
| issue = 1
| journal = Topology Proceedings
| mr = 2048922
| pages = 51–78
| department = Proceedings of the Spring Topology and Dynamical Systems Conference
| volume = 27
| year = 2003}}.
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