In this lecture note, we describe some properties of convex sets and their connection with a more general model in topological spaces. In particular, we discuss Tverberg's theorem, Borsuk's conjecture and related problems. First we give some basic properties of convex sets in R d. a i is also in S. Definition 2. Convex hull of a set A, denoted by conv(A), is the set of all convex combination of...