Abstract.
In this paper we mean by an Alexandroff space a topological space such that every point has a minimal neighborhood. We do not assume that the space is $T_0$. There spaces were first introduced by P. Alexandroff in 1937 in Ref. 1 and have become relevant for the study of digital topology. We make a systematic study of them from several points of view, including quasi-uniform spaces.
Compressed Postscript 
