Abstract. In this paper, we construct a cover (L(X), c X ) of a space X such that for any cloz-coverUsing this, we show that every Tychonoff space X has a minimal cloz-cover (E cc (X), z X ) and that for a strongly zero-dimensional space X, βE cc (X) = E cc (βX) if and only if Ecc(X) is z # -embedded in Ecc(βX).

In this paper, we consider the following functional equation with involutionand prove the generalized Hyers-Ulam stability for it when the target space is a non-Archimedean Banach space.