TITLE: $(x,y)\to xy$ continuous but $x\to x^{-1}$ not
QUESTION [12 upvotes]: In the definition of topological groups we impose both $(x,y)\to xy$ and $x\to x^{-1}$ to be continuous.
However, I cannot find an example where the first condition holds but the second fails.
Is the second one redundant?
Thanks!

REPLY [4 votes]: Sorgenfrey Line is another example of paratopological group. See: Topological group and related structure, Book by Arhangel'skii and Tkachenko Page 13 example 1.2.1.