Continuous Selections and Fixed Points for $ϕ$-Maps with Their Applications to Section Problems (Communications in Mathematical Research, 2021)
The concept of finitely continuous topological space is introduced andthe basic properties of the space are given. Several continuous selection theoremsand fixed point theorems for $ϕ$-maps are established, and as applications of the abovefixed point theorems, some section problems are discussed. The results generalize andimprove many corresponding conclusions.
Keywords: FC-space; FC-subset; $ϕ$-map; continuous selection; fixed point; section problem.