The total negation of a topological property

The central theme in this paper is the uniform generation of new topologi- cal properties from old. Two of the best known properties obtained in this way are total disconnectedness (deriving from connectedness) and scattered- ness (deriving from perfectness, i.e. having no isolated points). A third property, lesser known but interesting in its own right, is pseudofiniteness (the cf-spaces studied in [8], [9], [10], [12]) or the class of spaces whose compact subsets are finite. This last-mentioned property derives from com- pactness in the manner we will explore here.