Homeomorphism Groups and the Topologist's Sine Curve
Bulletin Polish Acad. Sci. Math. 58 (2010), 269-272 MSC: 54H11, 57S05. DOI: 10.4064/ba58-3-9
It is shown that deleting a point from the topologist's sine curve results in a locally compact connected space whose autohomeomorphism group is not a topological group when equipped with the compact-open topology.