A decomposition theorem for compact groups with an application to supercompactness

• Autorzy: Wiesław Kubiś , Sławomir Turek
• Języki publikacji: EN

Abstrakty

EN

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 As an application, we present a proof of an unpublished result of Charles Mills from 1978: every compact group is supercompact.

Słowa kluczowe

EN

Simple compact Lie group; Supercompact space

Kategorie tematyczne

• 54D30: Compactness
• 22C05: Compact groups
• 54H11: Topological groups

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2011
• Tom: 9
• Numer: 3
• Strony: 593-602

Daty

wydano

2011-06-01

online

2011-03-22

Twórcy

autor

Wiesław Kubiś

• Czech Academy of Sciences

autor

Sławomir Turek

• Jan Kochanowski University

Bibliografia

• [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
• [3] Kuz’minov V., On Alexandrov’s hypothesis in the theory of topological groups, Dokl. Akad. Nauk SSSR, 1959, 125, 727–729 (inRussian)
• [4] van Mill J., Supercompactness and Wallman Spaces, Math. Centre Tracts, 85, Mathematisch Centrum, Amsterdam, 1977
• [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
• [7] Strok M., Szymanski A., Compact metric spaces have binary bases, Fund. Math., 1975, 89, 81–91

Identyfikatory

DOI

10.2478/s11533-011-0019-x