D . Farley has shown that " F " acts as deck transformations on a locally finite CAT ( 0 ) cubical complex ( necessarily of infinite dimension ).
32.
His main interest was locally finite groups where he used his wide knowledge of finite groups to prove properties of infinite groups which shared some of the features of finite groups.
33.
On the other hand there is a theorem, to the effect that a subanalytic set " A " can be written as a locally finite union of submanifolds.
34.
An open cover of a space " X " is " locally finite " if every point of the space has a finitely many sets in the cover.
35.
One can check as an exercise that this provides an open refinement, since paracompact Hausdorff spaces are regular, and since \ mathcal { O } \, is locally finite.
36.
An abstract Wiener space is a mathematical object in measure theory, used to construct a " decent ", strictly positive and locally finite measure on an infinite-dimensional vector space.
37.
In "'simple symmetric random walk "'on a locally finite lattice, the probabilities of the location jumping to each one of its immediate neighbours are the same.
38.
Other M�bius inversion formulas are obtained when different locally finite partially ordered sets replace the classic case of the natural numbers ordered by divisibility; for an account of those, see incidence algebra.
39.
Much of the 1960s theory of formations and Fitting classes, as well as the older 19th century and 1930s theory of Sylow subgroups has an analogue in the theory of locally finite groups.
40.
The complex of curves is never locally finite ( each point belongs to infinitely many top-dimensional simplices ), in fact it is homotopically equivalent to a wedge sum of infinitely many spheres
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