Polynomial sequential continuity on C(k,e) spaces
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2003
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Elsevier
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Bombal Gordon, F. & Villanueva Díez, I. «Polynomial Sequential Continuity on C(K,E) Spaces». Journal of Mathematical Analysis and Applications, vol. 282, n.o 1, junio de 2003, pp. 341-55. DOI.org (Crossref), https://doi.org/10.1016/S0022-247X(03)00161-6.
Abstract
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.