CATEGORICAL DIRECTIONAL DENSITY AND SOME RELATED RESULTS

It has been proved by Bruckner2 that for a subset B of the Euclidean p lane R2 possessing the property of Baire, each point outside of some f irst category subset of B is a point of categorical directional densit y in all directions except, perhaps, a first category set of direction s. This paper begins with an introduction of a new definition of categ orical directional density which is followed by some related results t he first of which may be considered as a modification of Bruckner's th eorem.