Abstract: By using the well known KKM theorem on FC-spaces, an improved KKM type theorem was established and another form of KKM type theorem was given by introducing the definition of s-trappable, and then a continuous selection theorem on FC-space was obtained by the partition theorem of unity. Finally, several existence theorems of coincidence point were derived as the application of the aboveresults.

Key words: FC-space, FC-subspace, KKM map, upper semicontinuous, s-trappable