An Introduction to Relative Connectedness of Topological Spaces
摘要
In this paper, we introduce some versions of relative connectedness of subspaces of a topological space and we give some facts and relations among them. We prove that these relative versions satisfy some of the classical properties of connectedness. Additionally, we apply our results to the theory of hyperspaces, aiming to address a general problem posed by Arhangel’skii (Comment Math Univ Carolin 36:305–325, 1995, Problem 3).