Locally compact subgroup actions on topological groups
Por:
Antonyan, SA
Publicada:
1 ene 2013
Categoría:
Mathematics (miscellaneous)
Resumen:
Let X be a Hausdor topological group and G a locally compact subgroup of X. We show that X admits a locally finite s-discrete G-functionally open cover each member of which is G-homeomorphic to a twisted product G ×H Si, where H is a compact large subgroup of G (i.e., the quotient G=H is a manifold). If, in addition, the space of connected com- ponents of G is compact and X is normal, then X itself is G-homeomorphic to a twisted product G ×K S, where K is a maximal compact subgroup of G. This implies that X is K-homeomorphic to the product G=K×S, and in particular, X is homeomorphic to the product Rn ×S, where n = dimG/K. Using these results we prove the inequality dimX = dimX=G + dimG for every Hausdor topological group X and a locally compact subgroup G of X. © 2013 University of Houston.
Filiaciones:
Antonyan, SA:
Univ Nacl Autonoma Mexico, Fac Ciencias, Dept Matemat, Mexico City 04510, DF, Mexico
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