Abstract: In this paper,the following results are obtained: (1) The Sorgenfrey Line is a non-B_r- space; (2) We introduce Well-distributed complete spaces and locally Cech complete spaces and prove both the two classes of spacs are Br-spaces. The first result shows that there is the non-B_r- space which is paracompact, Lindelof and complete quasi-metric. The second result generalizes the Byczowski &. Pol theorem(i. e. Cech-complete spaces are Br-spaces) in two aspect... 

Key words:  B_r-spaces;Sorgenfrey Line;Well-distributed complete spaces;locally Cech-complete , spaces