Topology MOC

Sphere space

The -sphere is usually defined as the boundary of the unit ball in -dimensional Real coördinate space , topology i.e.

along with the subspace metric and subspace topology. It is thereby an -dimensional Topological manifold, and forms the boundary of the -Ball space.

Properties

• The -sphere is a Compact space.
• Retraction theorem: No retraction from ball to boundary sphere
• Borsuk-Ulam theorem: has a set of equal-valued antipodes

1-sphere

• Degree of a circle endomorphism

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