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In reference to this question:

This equation define a regular surface?

How can I prove that the union of this three plane is not a regular surface?

Intuitively this is clear.

Thanks!

Community
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EQJ
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1 Answers1

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You can prove a regular surface must at every point locally be a graph of some function over an open set in $xy$ or $yz$ or $xz$ plane.

Consider the origin and argue it can't be a graph of any function ( since it's multi-valued).

John
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