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  "body": "\n## Summary\n\nA semitopological group is a [[group|G5S1M9]] with a topology in which multiplication is continuous in each variable separately.\nEquivalently, every left translation and every right translation is continuous, and then each translation is a homeomorphism.\nIt weakens the notion of a [[topological group|92700QAB5Y]], which asks for joint continuity of multiplication and continuity of inversion.\nEllis's theorem says that a locally compact Hausdorff semitopological group is already a topological group.\n\n## Explanations\n\n### L1 human\n\nIn a semitopological group you may move one factor at a time and the product changes continuously.\nMoving both factors at once may cause a jump.\nA simple example is the group of integers under addition, with the topology in which the open sets are the empty set and the sets with finite complement.\nShifting by a fixed integer keeps such sets open, but addition of two varying integers is not continuous in this topology.\n",
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