... > topology > algebraic topology > manifold > differentiable manifold > Lie group > improper rotation

... > geometry > topological space > manifold > differentiable manifold > Lie group > improper rotation

geometry > differential geometry > differentiable manifold > Lie group > improper rotation

topology > differential topology > differentiable manifold > Lie group > improper rotation

algebra > group theory > topological group > Lie group > improper rotation

geometry > geometric transformation > isometry > improper rotation