It is proved that the square of the Sorgenfrey line has infinite covering dimension. Covering dimension dim was originally introduced by Lebesgue for domains in Euclidean spaces [1]. In 1933 Čech extended Lebesgue’s definition to completely regular spaces [2], and in 1950 Katětov proposed a different definition, which coincided with Čech’s one for normal spaces [3]. Since then, these two versions of covering dimension have become equally popular. Thus, the books [4], [5], and [6] use Čech’s… Expand