As the title says, why a spiral is the deformation retract of a plane?.
Why a spiral is the deformation retract of a plane?
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general-topology
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3How do you define a spiral? – 2011-10-28
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3Can you show that a half line is? Now conjugate that retraction with the homeomorphism that twists the entire plane such that the half line becomes a spiral. – 2011-10-28
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0@HenningMakholm And what if the spiral is doubly infinite? – 2011-10-28
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0@Phira, I'm implicitly assuming that it's an ordinary one-armed logarithmic or Archimedean spiral (including the center point because otherwise we're in trouble). If it has multiple arms, start instead by retracting into the union of the appropriate number of half lines radiating out from the origin. – 2011-10-28
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0I'm sorry I do not describe it clearly. Yes, it is an ordinary one-armed Archimedean spiral including the center point. I think it is easy to see that a plane can retract to a spiral without the center.But with a center, I find it not easy.. – 2011-10-29