Any neighborhood space is an open set topology and any open set topology is a neighborhood space. Seifert and Threlfall define a generic neighborhood space which is a superset of what is now generally used and related concepts and the following will show that those definitions apply to elements of .
Seifert and Threlfall do not allow neighborhood spaces on the empty set while sn0top is an example of a topology with an empty base set. This divergence is unlikely to pose serious problems.