Means on scattered compacta

• Autorzy: T. Banakh , R. Bonnet , W. Kubis
• Języki publikacji: EN

Abstrakty

EN

We prove that a separable Hausdor_ topological space X containing a cocountable subset homeomorphic to [0, ω1] admits no separately continuous mean operation and no diagonally continuous n-mean for n ≥ 2.

Słowa kluczowe

EN

Scattered compact space; mean operation

• Wydawca: De Gruyter Open
• Czasopismo: Topological Algebra and its Applications
• Rocznik: 2014
• Tom: 2
• Numer: 1

Daty

wydano

2014-01-01

otrzymano

2013-09-11

zaakceptowano

2014-04-04

online

2014-05-27

Twórcy

autor

T. Banakh

• Jan Kochanowski University in Kielce, Poland and Ivan Franko National University of Lviv, Ukraine

autor

R. Bonnet

• Laboratoire de Mathématiques, Université de Savoie, Le Bourget-du-Lac, France

autor

W. Kubis

• Institute of Mathematics, Academy of Sciences of the Czech Republic

Bibliografia

• [1] G. Aumann, Aufau von Mittelwerten mehrerer Argumente. II. (Analytische Mittelwerte), Math. Ann. 111:1 (1935), 713-730.
• [2] G. Aumann, Über Räume mit Mittelbildungen, Math. Ann. 119 (1944), 210-215.
• [3] G. Aumann, C. Carathéodory, Ein Satz über die konforme Abbildung mehrfach zusammenhängender ebener Gebiete, Math.Ann. 109 (1934), 756-763.
• [4] T. Banakh, O. Gutik, M. Rajagopalan, On algebraic structures on scattered compacta, Topology Appl. 153:5-6 (2005), 710-723.
• [5] R. Bonnet, W. Kubis, Semilattices, unpublished note.
• [6] B. Eckmann, Räume mit Mittelbildung, Comm. Math. Helv. 28 (1954), 329-340.
• [7] P. Hilton, A new look at means on topological spaces, Internat. J. Math. Math. Sci. 20:4 (1997), 617-620. [Crossref]
• [8] K. Hofmann, M. Mislove, A. Stralka, The Pontryagin duality of compact O-dimensional semilattices and its applications, Lecture Notes in Math., Vol. 396. Springer-Verlag, Berlin-New York, 1974.
• [9] I. Parovichenko, On a universal bicompactum of weight @, Dokl. Akad. Nauk SSSR, 150 (1963), 36-39.
• [10] A. Teleiko, M. Zarichnyi, Categorical Topology of Compact Hausdor_ spaces, VNTL Publ., Lviv, 1999.
• [11] F. Trigos-Arrieta, M. Turzanski, On Aumann’s theorem that the circle does not admit a mean, Acta Univ. Carolin. Math. Phys. 46:2 (2005), 77-82.

Identyfikatory

DOI

10.2478/taa-2014-0002