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  "body": "\n## Summary\n\nA locally connected space is a [[topological space|0CQHFPGJ45]] in which every point has arbitrarily small connected open [[neighbourhoods|0ZCY0Z80B6]].\nEquivalently, the [[connected components|0JG9W3KA6B]] of every open subset are open.\nLocal connectedness and [[connectedness|0V032VWTHD]] are independent: neither implies the other.\nIt is a hypothesis in many results of continuum theory, such as the [[Hahn–Mazurkiewicz theorem|Q5QFYKD004]].\n\n## Explanations\n\n### L1 human\n\nA space is locally connected if, zooming in near any point, you can always find a small open piece around it that is all in one piece.\nEuclidean space $\\R^n$ is locally connected, since small open balls are connected.\nTwo disjoint open intervals form a locally connected space that is not connected.\nThe [[comb space|A2Q4RXD162]] is connected but not locally connected.\n",
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