Means on scattered compacta

T. Banakh; R. Bonnet; W. Kubis

Topological Algebra and its Applications (2014)

  • Volume: 2, Issue: 1, page 5-10, electronic only
  • ISSN: 2299-3231

Abstract

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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.

How to cite

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T. Banakh, R. Bonnet, and W. Kubis. "Means on scattered compacta." Topological Algebra and its Applications 2.1 (2014): 5-10, electronic only. <http://eudml.org/doc/266591>.

@article{T2014,
abstract = {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.},
author = {T. Banakh, R. Bonnet, W. Kubis},
journal = {Topological Algebra and its Applications},
keywords = {Scattered compact space; mean operation; scattered compact space},
language = {eng},
number = {1},
pages = {5-10, electronic only},
title = {Means on scattered compacta},
url = {http://eudml.org/doc/266591},
volume = {2},
year = {2014},
}

TY - JOUR
AU - T. Banakh
AU - R. Bonnet
AU - W. Kubis
TI - Means on scattered compacta
JO - Topological Algebra and its Applications
PY - 2014
VL - 2
IS - 1
SP - 5
EP - 10, electronic only
AB - 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.
LA - eng
KW - Scattered compact space; mean operation; scattered compact space
UR - http://eudml.org/doc/266591
ER -

References

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  1. [1] G. Aumann, Aufau von Mittelwerten mehrerer Argumente. II. (Analytische Mittelwerte), Math. Ann. 111:1 (1935), 713-730. Zbl0012.25205
  2. [2] G. Aumann, Über Räume mit Mittelbildungen, Math. Ann. 119 (1944), 210-215. Zbl0060.40005
  3. [3] G. Aumann, C. Carathéodory, Ein Satz über die konforme Abbildung mehrfach zusammenhängender ebener Gebiete, Math.Ann. 109 (1934), 756-763. Zbl60.0285.04
  4. [4] T. Banakh, O. Gutik, M. Rajagopalan, On algebraic structures on scattered compacta, Topology Appl. 153:5-6 (2005), 710-723. Zbl1087.22003
  5. [5] R. Bonnet, W. Kubis, Semilattices, unpublished note. 
  6. [6] B. Eckmann, Räume mit Mittelbildung, Comm. Math. Helv. 28 (1954), 329-340. Zbl0056.16403
  7. [7] P. Hilton, A new look at means on topological spaces, Internat. J. Math. Math. Sci. 20:4 (1997), 617-620. [Crossref] Zbl0907.55010
  8. [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. Zbl0281.06004
  9. [9] I. Parovichenko, On a universal bicompactum of weight @, Dokl. Akad. Nauk SSSR, 150 (1963), 36-39. 
  10. [10] A. Teleiko, M. Zarichnyi, Categorical Topology of Compact Hausdor_ spaces, VNTL Publ., Lviv, 1999. Zbl1032.54004
  11. [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. 

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