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2answers
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Let $x\in \mathbb{R}$ and $z\in\mathbb{C}$. And define equality ($x=z$) iff $x=(0,x)$. Is this equality well defined?

Let $x\in \mathbb{R}$ and $z\in\mathbb{C}$. And define equality ($x=z$) iff $x=(0,x)$. Is this equality well defined ? Okay. It is easily shown that something goes wrong if you define equality in ...
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0answers
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Spherical Grid Identifcation

I'm trying to see how the lower half of these grids look like when I make the following identification onto the unit sphere: CLICK HERE TO SEE IMAGE In notation, how would one represent this ...
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1answer
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Is this an equivalence relation (reflexivity, symmetry, transitivity) (2)

The motivation to this question is: Is this an equivalence relation (reflexivity, symmetry, transitivity) : Let $\theta(s):\mathbb{C}\to \mathbb{R}$ be a well defined function. I define the ...
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2answers
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Is this an equivalence relation (reflexivity, symmetry, transitivity)

Let $\theta(s):\mathbb{C}\to \mathbb{R}$ be a well defined function. I define the following relation in $\mathbb{C}$. $\forall s,q \in \mathbb{C}: s\mathbin{R}q\iff\theta(s)\ne 0 \pmod {2\pi}$ (and) ...