Example of a quasitopological group with discontinuous power map - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-19T12:33:50Z http://mathoverflow.net/feeds/question/30769 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/30769/example-of-a-quasitopological-group-with-discontinuous-power-map Example of a quasitopological group with discontinuous power map Jeremy Brazas 2010-07-06T12:55:47Z 2010-07-12T10:21:06Z <p>A quasitopological group is a group $G$ with topology such that multiplication $G\times G\rightarrow G$ is continuous in each variable (i.e. all translations are continuous) and inversion $G\rightarrow G$ is continuous. Sometimes these are called semitopological or semicontinuous groups. What (if it exists) is an example of a quasitopological group such that at least one of the $n$-th power maps $g\mapsto g^{n}$ (for $n\geq 2$) is discontinuous?</p> <p>I am pretty sure such an example exists but I am having a hard time finding one in the literature.</p> http://mathoverflow.net/questions/30769/example-of-a-quasitopological-group-with-discontinuous-power-map/31523#31523 Answer by Mirek for Example of a quasitopological group with discontinuous power map Mirek 2010-07-12T10:21:06Z 2010-07-12T10:21:06Z <p>Maybe, the following topology on the plane works: a base at 0 is formed by the usual neighborhoods at 0 in the plane minus a convenient subset of the diagonal, e.g. the sequence 1/3^n (and -1/3^n). </p>