Self-Centred Sets
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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).
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2001 ◽
Vol 57
(4)
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pp. 471-484
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2007 ◽
Vol 62
(10)
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pp. 1235-1245
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1999 ◽
Vol 55
(4)
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pp. 607-616
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2021 ◽
Vol 77
(6)
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pp. 187-191
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Mathematical aspects of molecular replacement. IV. Measure-theoretic decompositions of motion spaces
2017 ◽
Vol 73
(5)
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pp. 387-402
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2016 ◽
pp. 24-38
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1969 ◽
Vol 21
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pp. 1309-1318
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1972 ◽
Vol 18
(1)
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pp. 81-83
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