Topological Transformation GroupsCourier Dover Publications, 13.06.2018 - 304 Seiten An advanced monograph on the subject of topological transformation groups, this volume summarizes important research conducted during a period of lively activity in this area of mathematics. The book is of particular note because it represents the culmination of research by authors Deane Montgomery and Leo Zippin, undertaken in collaboration with Andrew Gleason of Harvard University, that led to their solution of a well-known mathematical conjecture, Hilbert's Fifth Problem. The treatment begins with an examination of topological spaces and groups and proceeds to locally compact groups and groups with no small subgroups. Subsequent chapters address approximation by Lie groups and transformation groups, concluding with an exploration of compact transformation groups. |
Inhalt
CHAPTER | 1 |
CHAPTER II | 48 |
CHAPTER III | 106 |
CHAPTER IV | 153 |
CHAPTER V | 195 |
CHAPTER VI | 229 |
Bibliography | 272 |
Supplementary Bibliography | 280 |
| 287 | |
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Häufige Begriffe und Wortgruppen
abelian group Amer analytic arbitrarily small arbitrary borhood carrier circle group closed subgroup closed subset compact connected compact invariant subgroup compact neighborhood compact set compact subgroup completes the proof component connected group converges COROLLARY coset space countable cross-section defined denote differentiable dim G dimension element of G euclidean space example exists finite number finite-dimensional follows G/Go group G Hausdorff space Hence homeomorphism homogeneous space identity inner point integer inverse Lemma Let F Let G Let H Lie group linear locally compact group locally euclidean manifold Math matrix metric space natural map neigh one-one one-parameter group one-parameter local group open sets open subgroup orbit properties proved real number sequence shows small subgroups subgroup H subgroup of G Suppose symmetric neighborhood theorem three-space topological group topological space totally disconnected transformation group unique vector zero