And if we form the universal cover of this space, we get the following hyperbolic space (notice that I shrinked copies the the base space/“parallel universes”), because hyperbolic space does not fit into the Euclidean plane:
The fundamental group of \(X\) at \(x_0\) is \[\pi_1(X, x_0) \;:=\; \bigl\{[\gamma] \mid \gamma \text{ is a loop based at } x_0\bigr\}\] equipped with the group operation of concatenation: \[[\gamma] \cdot [\delta] := [\gamma * \delta], \qquad (\gamma * \delta)(s) := \begin{cases} \gamma(2s) & s \in [0,\tfrac{1}{2}] \\ \delta(2s-1) & s \in [\tfrac{1}{2},1] \end{cases}\] The identity element is the class of the constant loop \([c_{x_0}]\), and the inverse of \([\gamma]\) is \([\bar\gamma]\) where \(\bar\gamma(s) := \gamma(1-s)\).
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Квартиру в Петербурге затопило кипятком после обрушения потолка20:57
一、制定国家发展规划法的必要性和重大意义
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В Израиле одним словом оценили ход операции против Ирана14:58