In [1], we study coverings in the setting of directed topology. Unfortunately, there is a condition missing in the definition of a directed covering. Some of the results in [1] require this extra condition and in fact it was claimed to follow from the original definition. It is the purpose of this note to give the right definition and point out how this affects the statements in that paper. Moreover, we give an example of a dicovering in the sense of [1], which does not satisfy the extra condition. Fortunately, with the extra condition, the subsequent results are now correct.

[1] L. Fajstrup, Dicovering spaces, Homology Homotopy Appl. 5 (2003), no. 2, 1-17.