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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On closed additive semigroups in $ E\sp{n}$


Author: Christoph Bandelow
Journal: Proc. Amer. Math. Soc. 34 (1972), 87-89
MSC: Primary 22A15; Secondary 50A05, 60J15
MathSciNet review: 0292993
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Abstract: Let $ C(A)$ be the closed additive semigroup generated by a set $ A \subset {E^n}$. A simple necessary and sufficient condition on A for $ C(A)$ to be a group is derived. An example which arose in the theory of random walks and stimulated these purely geometrical considerations is discussed at the end.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0292993-3
Keywords: Closed additive semigroup in $ {E^n}$, closed additive group in $ {E^n}$, convex set, random walk
Article copyright: © Copyright 1972 American Mathematical Society