Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Semi-algebraic groups and the local closure of an orbit in a homogeneous space
HTML articles powered by AMS MathViewer

by Morikuni Goto PDF
Trans. Amer. Math. Soc. 247 (1979), 301-315 Request permission

Abstract:

Let L be a topological group acting on a locally compact Hausdorff space M as a transformation group. Let m be in M. A subset Q of M is called the local closure of the orbit Lm if Q is the smallest locally compact invariant subset of M with $m \in Q$. A partition \[ M = \bigcup \limits _{\lambda \in \wedge } {Q_\lambda }, {Q_{\lambda }} \cap {Q_\mu } = \emptyset \left ( {\lambda \ne \mu } \right )\] is called an LC-partition of M with respect to the L action if each ${Q_\lambda }$ is the local closure of Lm for any m in ${Q_\lambda }$. Theorem. Let G be a connected Lie group, and let A and B be subgroups of G with only finitely many connected components. Suppose that B is closed. Then the factor space $G/B$ has an LC-partition with respect to the A action.
References
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC: 57S20, 22D05
  • Retrieve articles in all journals with MSC: 57S20, 22D05
Additional Information
  • © Copyright 1979 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 247 (1979), 301-315
  • MSC: Primary 57S20; Secondary 22D05
  • DOI: https://doi.org/10.1090/S0002-9947-1979-0517696-X
  • MathSciNet review: 517696