# A decomposition theorem for compact groups with an application to supercompactness

Open Mathematics (2011)

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

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topWiesław 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 As an application, we present a proof of an unpublished result of Charles Mills from 1978: every compact group is supercompact.},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 As an application, we present a proof of an unpublished result of Charles Mills from 1978: every compact group is supercompact.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

top- [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] 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] 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] van Mill J., Supercompactness and Wallman Spaces, Math. Centre Tracts, 85, Mathematisch Centrum, Amsterdam, 1977 Zbl0407.54001
- [5] Mills C.F., Compact groups are supercompact, Free University of Amsterdam, Faculty of Mathematics, September 1978, seminar report
- [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] Strok M., Szymanski A., Compact metric spaces have binary bases, Fund. Math., 1975, 89, 81–91 Zbl0316.54030

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