The Van Kampen Theorem
In this section X will denote a connected, locally path-connected, and semilocally simply connected space, so X has a universal covering, denoted u:\(\tilde X\)→X. All spaces will have base points, and all maps will be assumed to take base points to base points. The base point of X is denoted x, and the base point of \(\tilde X\) over x is denoted \(\tilde x\).
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