Topological Space may be Empty
This convention is sufficiently commonplace as to be often omitted in published texts, and taken for granted. When it is mentioned, it is usually given as an afterthought.
Note, however, that many of the possible properties of a topological space are held vacuously by the empty space. This position having been taken, it is necessary in many cases to add a condition to a given general statement made about spaces specifically to exclude the empty space from the scope of that statement.