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Action | A Wisdom Archive on Action |  | Action A selection of articles related to Action |  |
| We recommend this article: Action - 1, and also this: Action - 2. |
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action, Action
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| ARTICLES RELATED TO Action | | | | | | | | | | | | |  |  |  | Action: Encyclopedia II - Group action - Types of actionsThe action of G on X is called
transitive if for any two x, y in X there exists an g in G such that g·x = y;
n-transitive if G acts transitively on Xn.
sharply n-transitive if G acts regularly on Xn.
faithful (or effective) if for any two different g, h ...
See also:Group action, Group action - Definition, Group action - Examples, Group action - Types of actions, Group action - Orbits and stabilizers, Group action - Morphisms and isomorphisms between G-sets, Group action - Continuous group actions, Group action - Strongly continuous group action and smooth vector, Group action - Generalizations Read more here: » Group action: Encyclopedia II - Group action - Types of actions |
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|  |  |  | Action: Encyclopedia II - Group action - Types of actionsThe action of G on X is called
transitive if for any two x, y in X there exists a g in G such that g·x = y;
n-transitive if G acts transitively on Xn.
sharply n-transitive if G acts regularly on Xn.
faithful (or effective) if for any two different g, h ...
See also:Group action, Group action - Definition, Group action - Examples, Group action - Types of actions, Group action - Orbits and stabilizers, Group action - Morphisms and isomorphisms between G-sets, Group action - Continuous group actions, Group action - Strongly continuous group action and smooth vector, Group action - Generalizations Read more here: » Group action: Encyclopedia II - Group action - Types of actions |
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| | | |  |  |  | Action: Encyclopedia II - Group action - Continuous group actionsOne often considers continuous group actions: the group G is a topological group, X is a topological space, and the map G × X → X is continuous with respect to the product topology of G × X. The space X is also called a G-space in this case. This is indeed a generalization, since every group can be considered a topological group by using the discrete topology. All the concepts introduced above still work in this context, however we define ...
See also:Group action, Group action - Definition, Group action - Examples, Group action - Types of actions, Group action - Orbits and stabilizers, Group action - Morphisms and isomorphisms between G-sets, Group action - Continuous group actions, Group action - Strongly continuous group action and smooth vector, Group action - Generalizations Read more here: » Group action: Encyclopedia II - Group action - Continuous group actions |
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