Algebraic & Geometric Topology Volume 11, issue 4 (2011)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

Submission form

Editorial board

Subscriptions

ISSN (electronic): 1472-2739

ISSN (print): 1472-2747

Author index

To appear

Other MSP journals

On the Chabauty space of locally compact abelian groups

Yves Cornulier

Algebraic & Geometric Topology 11 (2011) 2007–2035

DOI: 10.2140/agt.2011.11.2007

Bibliography

1	W Banaszczyk, New bounds in some transference theorems in the geometry of numbers, Math. Ann. 296 (1993) 625 MR1233487
2	N Bourbaki, Éléments de mathématique. Fascicule XXIX. Livre VI: Intégration. Chapitre 7: Mesure de Haar. Chapitre 8: Convolution et représentations, Actualités Scientifiques et Industrielles 1306, Hermann (1963) MR0179291
3	N Bourbaki, Éléments de mathématique. Fascicule XXXII. Théories spectrales. Chapitre I: Algébres normées. Chapitre II: Groupes localement compacts commutatifs, Actualités Scientifiques et Industrielles 1332, Hermann (1967) MR0213871
4	N Bourbaki, Éléments de mathématique. Topologie générale. Chapitres 1 à 4, Hermann (1971) MR0358652
5	D L Boyer, Enumeration theorems in infinite Abelian groups, Proc. Amer. Math. Soc. 7 (1956) 565 MR0078996
6	M R Bridson, P de la Harpe, V Kleptsyn, The Chabauty space of closed subgroups of the three-dimensional Heisenberg group, Pacific J. Math. 240 (2009) 1 MR2485473
7	C Chabauty, Limite d'ensembles et géométrie des nombres, Bull. Soc. Math. France 78 (1950) 143 MR0038983
8	C Champetier, L'espace des groupes de type fini, Topology 39 (2000) 657 MR1760424
9	Y de Cornulier, L Guyot, W Pitsch, On the isolated points in the space of groups, J. Algebra 307 (2007) 254 MR2278053
10	Y de Cornulier, L Guyot, W Pitsch, The space of subgroups of an abelian group, J. Lond. Math. Soc. $(2)$ 81 (2010) 727 MR2650794
11	J Dixmier, Quelques propriétés des groupes abéliens localement compacts, Bull. Sci. Math. $(2)$ 81 (1957) 38 MR0097457
12	R Engelking, Dimension theory, North-Holland Mathematical Library 19, North-Holland Publishing Co. (1978) MR0482697
13	S Fisher, P Gartside, On the space of subgroups of a compact group I, Topology Appl. 156 (2009) 862 MR2498918
14	S Fisher, P Gartside, On the space of subgroups of a compact group II, Topology Appl. 156 (2009) 855 MR2498917
15	R I Grigorchuk, Degrees of growth of finitely generated groups and the theory of invariant means, Izv. Akad. Nauk SSSR Ser. Mat. 48 (1984) 939 MR764305
16	T Haettel, L'espace des sous-groupes fermés de $\mathbb{R}{\times}\mathbb{Z}$, Algebr. Geom. Topol. 10 (2010) 1395 MR2661531
17	W Hurewicz, H Wallman, Dimension Theory, Princeton Mathematical Series 4, Princeton University Press (1941) MR0006493
18	J Isbell, Graduation and dimension in locales, from: "Aspects of topology", London Math. Soc. Lecture Note Ser. 93, Cambridge Univ. Press (1985) 195 MR787829
19	Y Katuta, On the covering dimension of inverse limits, Proc. Amer. Math. Soc. 84 (1982) 588 MR643755
20	B Kloeckner, The space of closed subgroups of $\mathbb{R}^n$ is stratified and simply connected, J. Topol. 2 (2009) 570 MR2546586
21	K Mahler, Ein Übertragungsprinzip für konvexe Körper, Časopis P\v est. Mat. Fys. 68 (1939) 93 MR0001242
22	L Narens, Topologies of closed subsets, Trans. Amer. Math. Soc. 174 (1972) 55 MR0312450
23	B A Pasynkov, The coincidence of various definitions of dimensionality for locally bicompact groups, Dokl. Akad. Nauk SSSR 132 (1960) 1035 MR0122906
24	I Pourezza, J Hubbard, The space of closed subgroups of $\mathbb{R}^{2}$, Topology 18 (1979) 143 MR544155
25	Ī V Protasov, Dualisms of topological abelian groups, Ukrain. Mat. Zh. 31 (1979) 207, 224 MR530080
26	Ī V Protasov, Y V Tsybenko, Connectedness in the space of subgroups, Ukrain. Mat. Zh. 35 (1983) 382 MR704344
27	I V Protasov, Y V Tsybenko, Chabauty's topology in the lattice of closed subgroups, Ukrain. Mat. Zh. 36 (1984) 207 MR742446
28	P Vopěnka, On the dimension of compact spaces, Czechoslovak Math. J. 8 (83) (1958) 319 MR0102068
29	F Wattenberg, Topologies on the set of closed subsets, Pacific J. Math. 68 (1977) 537 MR0500894