A class of nontrivial simple examples of a non-D-space

Given any regular T 0 {T_{0}} (equivalently, regular T 1 {T_{1}} ) space X, the question of whether X being Lindelöf implies X being a D-space is an active open problem. This article gives a class of handy examples of a second countable collectionwise normal collectionwise Hausdorff T 0 {T_{0}} space of uncountable cardinal, with at most countably many singletons being not closed, that is not a D-space. Also given is a class of handy examples of a second countable hyperconnected T 0 {T_{0}} space of uncountable cardinal, with at most countably many singletons being not closed, that is not a D-space.