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  "body": "\n## Summary\n\nA local homeomorphism is a map between [[topological spaces|0CQHFPGJ45]] that is a [[homeomorphism|0QT00PB5G2]] near each point, onto an open set.\nIt need not be injective or surjective as a whole.\nCovering maps and the projections of étale spaces are local homeomorphisms, and every local homeomorphism is [[continuous|0VGFHTM75Y]] and [[open|0YCG648KDD]].\n\n## Explanations\n\n### L1 human\n\nA local homeomorphism looks like a perfect copy when you only look at a small piece of the space.\nGlobally it may wrap the space around many times.\nThe map that winds the real line around the circle, sending $t$ to the point at angle $2\\pi t$, is the standard example.\nEach short interval goes onto an arc without any folding, but the whole line covers the circle infinitely often.\n",
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