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Properties of the so called ${\theta }_o$-complete topological spaces are investigated. Also, necessary and sufficient conditions are given so that the space $C(X,E)$ of all continuous functions, from a zero-dimensional topological space $X$ to a non-Archimedean locally convex space $E$, equipped with the topology of uniform convergence on the compact subsets of $X$ to be polarly barrelled or polarly quasi-barrelled.

Necessary and sufficient conditions are given so that the space $C(X,E)$ of all continuous functions from a zero-dimensional topological space $X$ to a non-Archimedean locally convex space $E$, equipped with the topology of uniform convergence on the compact subsets of $X$, to be polarly absolutely quasi-barrelled, polarly ${\aleph }_o$-barrelled, polarly ${\ell }^{\infty }$-barrelled or polarly $c_o$-barrelled. Also, tensor products of spaces of continuous functions as well as tensor products of certain $E^{\prime }$-valued measures are investigated.