In reminiscence of Ptak’s
open mapping theorem, a topological space satisfying the open mapping theorem is
called a Br space. This paper is devoted to the study of sums and products of Br
spaces in the category of topological spaces. We prove that, in general, sums and
products of even two Br spaces need no longer be Br. On the other hand, for any Br
space E the sum E ⊕ E is again a Br space. Moreover, since Čech complete spaces
are known to be Br, we ask whether a sum E ⊕ F is Br provided that E is Čech
complete and F is Br. It turns out that, at least in the framework of complete
regularity, the answer to this question is in the positive if and only if F is a Baire
space.
