Locally compact Hausdorff semitopological group implies topological group

History

The result is attributed to Ellis, and was proved in a paper by Ellis in 1957.

Statement

Suppose $G$ is a semitopological group whose underlying topological space is a locally compact Hausdorff space. Then, $G$ is in fact a topological group.

References

• Locally compact transformation groups by Robert Ellis, Duke Math Journal, Volume 24,Number 2, Page 119 - 125(Year 1957): ^{Project Euclid page (with ungated PDF download)More info}