Geodesic
On the existence of means on solenoids
Lobachevskii journal of mathematics, Tome 17 (2005), pp. 43-46.

Voir la notice de l'article provenant de la source Math-Net.Ru

A mean on a topological space is a continuous idempotent and symmetric operation on it. A proof of a criterion for the existence of means on solenoids is given.
Keywords: $n$-mean
Mots-clés : solenoid. 
@article{LJM_2005_17_a3,
     author = {R. N. Gumerov},
     title = {On the existence of means on solenoids},
     journal = {Lobachevskii journal of mathematics},
     pages = {43--46},
     publisher = {mathdoc},
     volume = {17},
     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/LJM_2005_17_a3/}
}
TY  - JOUR
AU  - R. N. Gumerov
TI  - On the existence of means on solenoids
JO  - Lobachevskii journal of mathematics
PY  - 2005
SP  - 43
EP  - 46
VL  - 17
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/LJM_2005_17_a3/
LA  - en
ID  - LJM_2005_17_a3
ER  - 
%0 Journal Article
%A R. N. Gumerov
%T On the existence of means on solenoids
%J Lobachevskii journal of mathematics
%D 2005
%P 43-46
%V 17
%I mathdoc
%U http://geodesic.mathdoc.fr/item/LJM_2005_17_a3/
%G en
%F LJM_2005_17_a3
R. N. Gumerov. On the existence of means on solenoids. Lobachevskii journal of mathematics, Tome 17 (2005), pp. 43-46. http://geodesic.mathdoc.fr/item/LJM_2005_17_a3/

[1] Kolmogoroff A. N., “Sur la notion de la moyenne”, Atti Acad. Naz. Lincei. Rend. Cl. Sci. Fis. Mat. Nat. (6), 12 (1930), 388–391 | Zbl

[2] Aumann G., “Über Räume mit Mittelbildungen”, Math. Ann., 119 (1944), 210–215 | DOI | MR | Zbl

[3] Eckmann B., “Räume mit Mittelbildungen”, Comment. Math. Helv., 28 (1954), 329–340 | DOI | MR | Zbl

[4] Keesling J., “The group of homeomorphisms of a solenoid”, Trans. Amer. Math. Soc., 172 (1972), 119–131 | DOI | MR

[5] Krupski P., “Means on solenoids”, Proc. Amer. Math. Soc., 131 (2002), 1931–1933 | DOI | MR

[6] McCord M. C., “Inverse limit sequences with covering maps”, Trans. Amer. Math. Soc., 114 (1965), 197–209 | DOI | MR | Zbl

[7] Hewitt E., Ross K. A., Abstract harmonic analysis, Vol. I, Springer–Verlag, Berlin, 1963 | MR | Zbl

[8] Scheffer W. A., “Maps between topological groups that are homotopic to homomorphisms”, Proc. Amer. Math. Soc., 33 (1972), 562–567 | DOI | MR | Zbl

[9] Gumerov R. N., “On finite-sheeted covering mappings onto solenoids”, Proc. Amer. Math. Soc., 133:9 (2005), 2771–2778 | DOI | MR | Zbl

[10] Aarts J. M., Fokkink R. J., “Mappings on the dyadic solenoid”, Comment. Math. Univ. Carolinae, 44:4 (2003), 697–699 | MR | Zbl

[11] Gumerov R. N., “Means on compact groups”, International Conference, Kazan Math. Soc., Trudy Lobachevskii Centre Math., 25, 2004, 97–98 (Russian)