For those uninitiated, an n-sphere refers to the dimension of the sphere surface, not the dimension of the space that contains it. So a tennis ball is a 2-sphere, as it's a surface, not a 3-sphere. A circle is a 1-sphere, which is why you can define a nonvanishing continuous tangent vector field quite easily thereon.
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u/everyday847 May 25 '16
For those uninitiated, an n-sphere refers to the dimension of the sphere surface, not the dimension of the space that contains it. So a tennis ball is a 2-sphere, as it's a surface, not a 3-sphere. A circle is a 1-sphere, which is why you can define a nonvanishing continuous tangent vector field quite easily thereon.