Transactions of the American Mathematical Society

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

Author(s): B. Bordbar; J. Pym
Journal: Trans. Amer. Math. Soc. 352 (2000), 823-842.
MSC (1991): Primary 43A60, 22A15; Secondary 22D05
Posted: July 20, 1999
Retrieve article in: PDF
This article is available free of charge

Abstract: This paper answers negatively the question of whether the sets of idempotents in the weakly almost periodic compactifications of $(\mathbb{N}, +)$ and $(\mathbb{Z} ,+)$ are closed.

1.: J F Berglund, Problems about semitopological semigroups, Semigroup Forum 16 (1980), 373-383. MR 81f:20098
2.: B Bordbar, Weakly almost periodic functions on $\mathbb N$ with a negative base, J 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 I\c{s}ik and J Pym, Subsemigroups of Stone-\v{C}ech 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 $\kappa$ -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-\v{C}ech Compactification, de Gruyter, Berlin, 1998.
10.: T Papazyan, Oids, finite sums and the structure of the Stone-\v{C}ech compactification of a discrete semigroup, Semigroup Forum 42 (1991), 265-277. MR 92b:54051
11.: J S Pym, Semigroup structure in Stone-\v{C}ech 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 ${\mathfrak{a}}$ -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 Banach spaces, Proc Roy Irish Acad A 67 (1968), 27-37. MR 39:824

Retrieve articles in Transactions of the American Mathematical Society with MSC (1991): 43A60, 22A15, 22D05

B. Bordbar
Affiliation: Department of Pure Mathematics, University of Sheffield, Sheffield S3 7RH, England
Email: j.pym@sheffield.ac.uk

J. Pym
Affiliation: Department of Pure Mathematics, University of Sheffield, Sheffield S3 7RH, England

DOI: 10.1090/S0002-9947-99-02273-4
PII: S 0002-9947(99)02273-4
Keywords: weakly almost periodic, semigroup compactification, idempotent
Received by editor(s): June 16, 1997
Posted: July 20, 1999
Copyright of article: Copyright 1999, American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support Help
ISSN 1088-6850(e) ISSN 0002-9947(p)

Previous issue \| Table of contents \| Next issue Articles in press \| Recently posted articles \| Most recent issue \| All issues Previous Article \| Next Article


	Comments: webmaster@ams.org © Copyright 2009, American Mathematical Society Privacy Statement		Search the AMS