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  "body": "\n## Summary\n\nA topological transformation group is a [[topological group|92700QAB5Y]] acting on a topological space so that the action map is continuous.\nIt is the topological version of a [[group action|0WCY42EV9V]], and it is the basic object of topological dynamics.\nEach group element then acts by a homeomorphism of the space.\nHomogeneous spaces, flows and actions of Lie groups on manifolds are all examples.\n\n## Explanations\n\n### L1 human\n\nA group can move the points of a space around: rotations move the points of a sphere, for example.\nIn a topological transformation group, the motion depends continuously both on the group element and on the point.\nRotating by a slightly different angle, or starting at a slightly different point, changes the result only slightly.\nThe rotation group acting on the sphere is the standard picture.\n",
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