The set of idempotents in the weakly almost periodic compactification of the integers is not closed

Transactions of the American Mathematical Society

Volumn 352, Issue 2, 2000, Pages 823-842

  Bordbar, B ^a   Pym, J ^a  

^a UNIVERSITY OF SHEFFIELD   (United Kingdom)

Author keywords

Idempotent; Semigroup compactification; Weakly almost periodic

Indexed keywords

EID: 22844457312     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9947-99-02273-4     Document Type: Article

References (15)

1. J F Bcrglund, Problems about semitopological semigroups, Semigroup Forum 16 (1980), 373383. MR 81f:20098
2. B Bordbar, Weakly almost periodic functions on N with a negative base, 3 London Math Soc (to appear).
3. B Bordbar and J Pym, The weakly almost periodic compactification of a direct sum of finite groups, Math Proc Cambridge Phil Soc 124 (1998), 421-449. CMP 98:16
4. G Brown and W Moran, The idempotent semigroups of compact monothetic semigroups, Proc. Roy. Irish Acad., Sect. A , 72 (1972), 17-33. MR 46:3682
5. T Budak, N Iik and J Pym, Subsemigroups of Stone-Cech compactifications, Math. Proc. Camb. Phil. Soc. 99 (1994), 116-137. MR 94c:54067
6. K de Leeuw and I Glicksberg, Applications of almost periodic compactifications, Acta Math 105 (1961), 63-97. MR 24:A1632
7. G A Edgar, Measure, Topology and Fractal Geometry, Springer, Berlin, 1990. MR 92a:54001
8. N Hindman, The ideal structure of the space of K-uniform ultrafilters on a discrete semigroup, Rocky Mountain Math J 16 (1986), 685-701. MR 88d:54031
9. N Hindman and D Strauss, Algebra in the Stone-Cech Compactification, de Gruyter, Berlin, 1998.
10. T Papazyan, Oids, finite sums and the structure of the Stone-Cech Compactification of a discrete semigroup, Semigroup Forum 42 (1991), 265-277. MR 92b:54051
11. J S Pym, Semigroup structure in Stone-Cech compactifications, J. London Math. Soc. 36 (1987), 421-428. MR 89b:54043
12. W A F Ruppert, Compact Semitopological Semigroups: An Intrinsic Theory, Lecture Notes in Mathematics 1079, Springer, Berlin, 1984. MR 86e:22001
13. W A F Ruppert, Compact semitopological semigroups, The Analytical and Topological Theory of Semigroups (K H Hofmann, J D Lawson and J S Pym, eds.), de Gruyter, Berlin, 1990, pp. 133-170. MR 91i:22006
14. W A F Ruppert, On signed a-adic expansions and weakly almost periodic functions, Proc. London Math. Soc. 63 (1991), 620-656. MR 93c:43007
15. T T West, Weakly compact monothetic semigroups of operators in Danach spaces, Proc Roy Irish Acad A 67 (1968), 27-37. MR 39:824