VARIOUS EXAMPLES OF THE KKM SPACES

Recall that a partial KKM space is a topological space satisfying an abstract form of the well-known KKM theorem, and a KKM space is a partial KKM space satisfying the 'open-valued' version of the form. Recently, we have found several new examples of such spaces. As a continuation of the preceding two works, we are going to introduce old and new examples of the KKM spaces, which play a major role in applications of the KKM theory. Finally, we state why we should use triples (X, D; Gamma) for abstract convex spaces by giving further examples, and introduce an example of a partial KKM space which is not a KKM space.