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  "body": "\n## Summary\n\nA paratopological group is a [[group|G5S1M9]] with a topology in which multiplication is jointly continuous, while inversion need not be continuous.\nIt sits between a [[semitopological group|5WGMRS4JSE]] and a [[topological group|92700QAB5Y]].\nThe standard example that is not a topological group is the real line under addition with the lower limit topology.\nMuch of the theory asks which extra conditions force inversion to be continuous.\n\n## Explanations\n\n### L1 human\n\nIn a paratopological group, multiplying nearby elements gives nearby results, but taking inverses may tear the space apart.\nPicture the real line where the basic open sets are the half-open intervals $[a, b)$.\nAdding two numbers still behaves well: if $x$ and $y$ move a little to the right, so does $x + y$.\nBut the map $x \\mapsto -x$ turns intervals $[a, b)$ into intervals $(-b, -a]$, which are not open in this topology.\n",
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