Polynomial sequential continuity on C(K,E) spaces ✩

We show that, for bounded sequences in C(K,E), the polynomial sequential convergence is not equivalent to the pointwise polynomial sequential convergence.We introduce several conditions on E under which different versions of the result are true when K is a scattered compact space. These conditions are related with some others appeared in the literature and they seem to be of independent interest.  2003 Elsevier Science (USA). All rights reserved