A general approach to the theory of set-valued mappings
The main goal of this paper is to establish a technical result, which provides an algorithm to prove several cardinal inequalities and relative versions of cardinal inequalities related to the well-known Arhangel’skii’s inequality: If is a -space, then . Moreover, we will show relative versions of three well-known cardinal inequalities.
A metric space is called a space provided each continuous function on into a metric target space is uniformly continuous. We introduce a class of metric spaces that play, relative to the boundedly compact metric spaces, the same role that spaces play relative to the compact metric spaces.