A decomposition theorem for compact groups with an application to supercompactness

Wiesław Kubiś; Sławomir Turek

Open Mathematics (2011)

  • Volume: 9, Issue: 3, page 593-602
  • ISSN: 2391-5455

Abstract

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We show that every compact connected group is the limit of a continuous inverse sequence, in the category of compact groups, where each successor bonding map is either an epimorphism with finite kernel or the projection from a product by a simple compact Lie group. As an application, we present a proof of an unpublished result of Charles Mills from 1978: every compact group is supercompact.

How to cite

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Wiesław Kubiś, and Sławomir Turek. "A decomposition theorem for compact groups with an application to supercompactness." Open Mathematics 9.3 (2011): 593-602. <http://eudml.org/doc/268942>.

@article{WiesławKubiś2011,
abstract = {We show that every compact connected group is the limit of a continuous inverse sequence, in the category of compact groups, where each successor bonding map is either an epimorphism with finite kernel or the projection from a product by a simple compact Lie group. As an application, we present a proof of an unpublished result of Charles Mills from 1978: every compact group is supercompact.},
author = {Wiesław Kubiś, Sławomir Turek},
journal = {Open Mathematics},
keywords = {Simple compact Lie group; Supercompact space; compact group; compact connected group; simple compact Lie group; supercompact space},
language = {eng},
number = {3},
pages = {593-602},
title = {A decomposition theorem for compact groups with an application to supercompactness},
url = {http://eudml.org/doc/268942},
volume = {9},
year = {2011},
}

TY - JOUR
AU - Wiesław Kubiś
AU - Sławomir Turek
TI - A decomposition theorem for compact groups with an application to supercompactness
JO - Open Mathematics
PY - 2011
VL - 9
IS - 3
SP - 593
EP - 602
AB - We show that every compact connected group is the limit of a continuous inverse sequence, in the category of compact groups, where each successor bonding map is either an epimorphism with finite kernel or the projection from a product by a simple compact Lie group. As an application, we present a proof of an unpublished result of Charles Mills from 1978: every compact group is supercompact.
LA - eng
KW - Simple compact Lie group; Supercompact space; compact group; compact connected group; simple compact Lie group; supercompact space
UR - http://eudml.org/doc/268942
ER -

References

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  1. [1] van Douwen E. K., van Mill J., Supercompactspaces, Topology Appl., 1982, 13(1), 21–32 http://dx.doi.org/10.1016/0166-8641(82)90004-9 
  2. [2] Hofmann K. H., Morris S. A., The Structure of Compact Groups, 2nd ed., de Gruyter Stud. Math., 25, de Gruyter, Berlin, 2006 Zbl1139.22001
  3. [3] Kuz’minov V., On Alexandrov’s hypothesis in the theory of topological groups, Dokl. Akad. Nauk SSSR, 1959, 125, 727–729 (inRussian) Zbl0133.28704
  4. [4] van Mill J., Supercompactness and Wallman Spaces, Math. Centre Tracts, 85, Mathematisch Centrum, Amsterdam, 1977 Zbl0407.54001
  5. [5] Mills C.F., Compact groups are supercompact, Free University of Amsterdam, Faculty of Mathematics, September 1978, seminar report 
  6. [6] Mills C.F., van Mill J., A nonsupercompact continuous image of a supercompact space, Houston J. Math., 1979, 5(2), 241–247 Zbl0423.54012
  7. [7] Strok M., Szymanski A., Compact metric spaces have binary bases, Fund. Math., 1975, 89, 81–91 Zbl0316.54030

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