Equivalence of the ap-Sequential Henstock and ap-Sequential Topological Henstock Integrals

Abstract

Let $X$ be a topological space and $\Omega \subset X$. Suppose $f:\Omega\rightarrow X$ is a function defined in a complete space $ \Omega $ and $ \tau $ is a vector in $ \mathbb{R} $ taking values in $X$. Suppose $ f $ is ap-Sequential Henstock integrable with respect to $\tau$, is $ f $ ap-Sequential Topological Henstock integrable with respect to $\tau$? It is the purpose of this paper to proffer affirmative answer to this question.