: Mathematics: one-parameter subgroup

... > algebraic topology > manifold > differentiable manifold > Lie group > one-parameter subgroup

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geometry > differential geometry > differentiable manifold > Lie group > one-parameter subgroup

topology > differential topology > differentiable manifold > Lie group > one-parameter subgroup

algebra > group theory > topological group > Lie group > one-parameter subgroup

one-parameter subgroup

In mathematics, a one-parameter group or one-parameter subgroup usually means a continuous group homomorphism
${\\displaystyle \\varphi :\\mathbb {R} \ ightarrow G}$

from the real line ${\\displaystyle \\mathbb {R} }$ (as an additive group) to some other topological group ${\\displaystyle G}$ . If ${\\displaystyle \\varphi }$ is injective then ${\\displaystyle \\varphi (\\mathbb {R} )}$ , the image, will be a subgroup of ${\\displaystyle G}$ that is isomorphic to ${\\displaystyle \\mathbb {R} }$ as an additive group.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/One-parameter_group)

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