B Mapping wave forms to sphere, does wave form y=0 have a reflection?

bahamagreen
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Continuous mapping of all continuous wave forms to the surface of a sphere
Zero does not have an inverse.
And y=0 does not have an inverse.
Does the wave form y=0 for all x have an inverse?
 
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What conditions should an inverse of a 'wave form' fulfil ?
:wideeyed:

##\ ##
 
BvU said:
What conditions should an inverse of a 'wave form' fulfil ?
:wideeyed:

##\ ##
My first thought is inverse polarity, but if the inverse wave form comprises -y values, any y=0 wouldn't have an inverse -y, so maybe the inverse wave form would not be strictly continuous? That seems asymmetric with respect to inversion...

edit-- I'm using the wrong term, inversion swaps the range and domain, what I am asking about is reflection about the x axis... y -> -y
This is in the context of antipodean pairs on the sphere
 
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More checking, but it looks like zero does have reflection...
 
A sphere as topological manifold can be defined by gluing together the boundary of two disk. Basically one starts assigning each disk the subspace topology from ##\mathbb R^2## and then taking the quotient topology obtained by gluing their boundaries. Starting from the above definition of 2-sphere as topological manifold, shows that it is homeomorphic to the "embedded" sphere understood as subset of ##\mathbb R^3## in the subspace topology.

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