Epimorphisms of compact groups are onto
Author:
Detlev Poguntke
Journal:
Proc. Amer. Math. Soc. 26 (1970), 503-504
MSC:
Primary 22.60
DOI:
https://doi.org/10.1090/S0002-9939-1970-0263978-6
MathSciNet review:
0263978
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: It is proved that the epimorphisms in the category of compact groups are surjective. The proof is based on the representation theory of compact groups, especially on the well-known fact, that for a closed proper subgroup 
of a compact group 
there exists an irreducible representation of 
which, when restricted to 
, contains the unit representation.
Retrieve articles in Proceedings of the American Mathematical Society with MSC: 22.60
Retrieve articles in all journals with MSC: 22.60
Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1970-0263978-6
Keywords:
Epimorphisms,
category,
compact groups,
finite-dimensional representations,
unitary transformations
Article copyright:
© Copyright 1970
American Mathematical Society