Almost strongly θ-precontinuous functions

In this paper, we introduce a new class of functions called almost strongly θ-precontinuous function which is a generalization of almost strongly θ-continuous functions due to Noiri and Kang [Noiri T, Kang SM. On almost strongly θ-continuous functions. Indian J Pure Appl Math 1984;15(1):1–8] and strongly θ-precontinuous functions due to Noiri [Noiri T. Strongly θ-precontinuous functions. Acta Math Hung 2001;90(4):307–16]. Some characterizations and several properties concerning almost strongly θ-precontinuous functions are obtained. The relationships between almost strongly θ-precontinuity and other types of continuity are also given.