Abstract
This is a brief survey on almost injectivity that has been studied mostly by Harada, and his collaborators. Baba introduced this concept as a dual to the concept of almost projectivity. In this survey, we state salient results by main contributors on this topic and some recent results by the authors. This exposition is not claimed to be exhaustive but is meant to highlight important discoveries made in the area and to point out future possible work. A list of open questions is given. The interested readers, particularly graduate students, would benefit most by going over the wealth of information contained in the referenced papers on almost injectivity and projectivity.