A note on almost contra-precontinuous functions

Almost contra-precontinuous functions were introduced by Ekici [7] and recently have been investigated further by Noiri and Popa [13]. The purpose of this note is to develop some new characterizations of almost contra-precontinuous functions and to introduce a new weak form of almost contra-precontinuity, which we call subalmost contraprecontinuity. It is shown that subalmost contra-precontinuity implies subalmost weak continuity and is independent of subweak continuity. Subalmost contra-precontinuity is used to extend several results in the literature concerning almost contra-precontinuity. For example, we show that the graph of a subalmost contra-precontinuous function with a Hausdorff codomain is P-regular and that the domain of a subalmost contraprecontinuous injection with a weakly Hausdorff codomain is pre-T1. These results extend the analogous results for an almost contra-precontinuous function.