Connectedness of suns in the space c(0)

摘要

We study the question of the connectedness of suns in the space c(0). We show that any sun M in c(0) is m-connected (in the sense of Brown). It follows that M is monotonically path-connected and the intersection of M with an arbitrary ball in c(0) is monotonically path-connected (and, in particular, path-connected). On the other hand, we establish that every approximatively compact m-connected set in c(0) is a sun in c(0). For X = c(0), c or l(infinity), it is proved that the intersection of a sun in X with a finite-dimensional coordinate subspace H-n subset of X is a P-acyclic sun in H-n.