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| ==Definition==
| | #redirect [[semitopological group]] |
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| A '''quasitopological group''' is a [[group]] <math>G</math> whose underlying set is endowed with the structure of a [[topological space]] such that:
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| # the inverse map is a continuous map from <math>G</math> to itself, and
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| # the group multiplication is a separately continuous map, i.e., for any fixed <math>g \in G</math>, the maps <math>h \mapsto gh</math> and <math>h \mapsto hg</math> are both continuous.
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| Note that in place of condition (2), it suffices to require that the group multiplication be continuous in the left coordinate. It also suffices to require that the group operation be continuous in its right coordinate.
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