For instance, if I want to describe the position on a circle I can write that the angle $\theta$ can be found in the interval $[0, \tau)$, but how can I express that this interval is periodic, e.g. that $0$ and $\tau^-$ are "glued" together?
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1Do you mean $\theta \in [0+ 2k\pi, \tau + 2k\pi)$ for some $k \in \mathbb Z$? – Eman Yalpsid Mar 29 '17 at 13:49
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@Andrew that seems appropriate, but needlessly complicated. – Frank Vel Mar 29 '17 at 13:52
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1How about $[0,\tau) + 2\pi \mathbb Z$ then? – Eman Yalpsid Mar 29 '17 at 13:54
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As Andrew suggested, you can write: $$ [0,\tau)\ +\ 2\pi\mathbb{Z} $$ or using quotient spaces notation: $$ [0,\tau)\ /\ 2\pi\mathbb{Z} $$
Jonathan H
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