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Definition 3 A universal cover of a topological space \(X\) is a covering space \(\tilde{X}\) of \(X\) that is simply connected, meaning that it has no nontrivial loops. The universal cover is unique up to homeomorphism and serves as a “universal” object in the category of covering spaces of \(X\).
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Now that we can build the tree, let's use it to search. Finding a specific point means starting at the root and asking: which child quadrant contains this coordinate? Then you recurse into that child and ask again. Each level of the tree cuts the search space by roughly three-quarters.
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