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- About the ##SO(3)## topology as subset/subspace topology from ##\mathbb R^9##
##SO(3)## is a Lie group of dimension 3. It is the set of 3x3 matrices ##R## with the following properties: $$RR^T = R^TR=I, \text{det}(R)=+1$$ There exists a parametrization of ##SO(3)## that maps it on the sphere in ##\mathbb R^3## of radius ##\pi## where the antipodal points are identified. This map is bijective and it basically defines the topology of ##SO(3)## -- i.e. let me say the map is homeomorphism by definition.
Is this the subspace topology from ##\mathbb R^9## on ##SO(3)## as subset of ##\mathbb R^9## ?
Is this the subspace topology from ##\mathbb R^9## on ##SO(3)## as subset of ##\mathbb R^9## ?
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