Self-Centred Sets
Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 974-980
Voir la notice de l'article provenant de la source Cambridge University Press
A subset S of an abelian group G is said to have a centre at a if whenever x belongs to S so does 2a — x. This note is mainly concerned with self-centred sets, i.e. those S with the property that every element of S is a centre of S. Such sets occur in the study of space groups: the set of inversion centres of a space group is always self-centred. Every subgroup of G is self-centred, so is every coset in G: this is the reason why the set of points of absolute convergence of a trigonometric series is self-centred or empty (1). A self-centred set of real numbers that is either discrete or consists of rational numbers must in fact be a coset (see §3); this does not hold for an arbitrary enumerable self-centred set of real numbers (§3.3).
Kestelman, H. Self-Centred Sets. Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 974-980. doi: 10.4153/CJM-1966-098-3
@article{10_4153_CJM_1966_098_3,
author = {Kestelman, H.},
title = {Self-Centred {Sets}},
journal = {Canadian journal of mathematics},
pages = {974--980},
year = {1966},
volume = {18},
number = {1},
doi = {10.4153/CJM-1966-098-3},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1966-098-3/}
}
[1] 1. Arbault, J., Sur l'ensemble de convergence absolue d'une série trigonométrique, Bull. Soc. Math. France, 80 (1952), 253–317. Google Scholar
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