ALMOST TRANSITIVITY IN $mathcal{C}_0$ SPACES OF VECTOR-VALUED FUNCTIONS

摘要

By means of $M$-structure and dimension theory, we generalize some known results and obtain some new ones on almost transitivity in $mathcal{C}_0(L,X)$. For instance, if $X$ has the strong Banacha€“Stone property, then almost transitivity of $mathcal{C}_0(L,X)$ is divided into two weaker properties, one of them depending only on topological properties of $L$ and the other being closely related to the covering dimensions of $L$ and $X$. This leads to some non-trivial examples of almost transitive $mathcal{C}_0(L,X)$ spaces.