The DOI matches its Crossref record; 2 of the 2 references it cites were found in a registry or an index.
Simply connected homogeneous spaces
Open accessAbstract
Introduction. Let G be a topological group which acts transitively, as a transformation group, on a space M. If x is any point of M, let G, be the closed subgroup made up of all elements in G which leave x fixed. There is a natural one-to-one correspondence between points of M and points of the coset space or homogeneous space G/G.. This one-to-one correspondence is not a homeomorphism in the most general cases, but it is clearly a homeomorphism if G is a compact Lie group, and it is also a homeomorphism if G is a Lie group and M is a manifold [1].' In the present note the following theorem will be proved:
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Citations
Cites
On Some Types of Topological Groups
Iwasawa, K. (1949) · Annals of Mathematics · doi:10.2307/1969548 · Cited by 630
Topologies for Homeomorphism Groups
Arens, R. F. (1946) · American Journal of Mathematics · doi:10.2307/2371787 · Cited by 277
Flagged first, then by citations
Research works printed but not linked: 1
- Mostow, George Daniel, 1950, The extensibility of local Lie groups of transformations and groups on surfaces, Ann. of Math. (2), 52, 606, 10.2307/1969437 · DOI
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Samelson, H. (1952) · Bulletin of the American Mathematical Society · doi:10.1090/s0002-9904-1952-09544-6 · Cited by 219
Metadata
- Authors
- Montgomery, D.
- Corresponding author
- Montgomery, Deane
- Venue
- Proceedings of the American Mathematical Society
- Publisher
- American Mathematical Society (AMS)
- Published
- 1950-08
- Volume
- 1
- Issue
- 4
- Pages
- 467-469
- ISSN
- 0002-9939 (ISSN-L)
- 1088-6826
- OpenAlex
- W2024311958
- Cited by
- 100
- References
- 2
- Citations by year
- 2025: 2 · 2024: 1 · 2023: 2 · 2022: 2 · 2021: 3 · 2020: 2 · 2019: 4 · 2018: 3 · 2016: 1 · 2013: 1 · 2012: 3
- FWCI
- 7.72
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Proceedings of the American Mathematical Society (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Geometry and Topology › Advanced Differential Geometry Research
- Physical Sciences › Mathematics › Algebra and Number Theory › Advanced Algebra and Geometry
- Physical Sciences › Mathematics › Geometry and Topology › Geometric and Algebraic Topology
- Keywords
- homogeneous spaces, topological groups, transitive group actions, coset spaces, compact Lie groups, Lie groups, manifolds, homeomorphism
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