In the above mentioned paper, the remarks 5.2, as stated, are erroneous. Part (b) of it should read "CL(U) E fl,~l~,i-~t To(x) means exactly that p(x) must be an open neighbourhood of x in (X, FL-,))". Part (a) should be postponed, under a modified form, until after Proposition 5.4. This has no bearing on the proof of 5.3, so this proposition remains valid (giving N*(x) the same meaning as in 5.1). The proof of 5.4 must be slightly adapted as follows. In parts (a), (b), (c) of that proof, &(x) should stand, temporarily, for {~*;~:Z,+2Xdecreasing and VCYEZ~:~((Y) ~&l,,~-~l 'Q(x)}.
If then N(x) is the (non-empty) set of all fuzzy neighbourhood systems on X with level-topologies (F= = l,(t('Y(x)))),;,,, and (X(X)),,~ is an arbitrary member of N(X), then part (a) of the proof in fact means that X(x) c J&(X). The rest of the proof remains unaltered, and parts (a), (b), (c) together give X(x) c N*(x) c Y(x). From this it follows:
- by arbitrariness of X(x) that X(x) = N&x) = V(x); 2. that N(X) is a singleton (i.e. in fact, Theorem 5.5), and therefore that N,(x) can be given again the same meaning as in 5.3; 3. (modified remark 5.2(a)) (C&$(x)),,, is a basis for (Sr(x)& and C&(x) = "c"(x), but only if (Fa)nel, is a descending chain that has the (LT)-property.
It should be noted also that in Remark 3.4(c) there is an evident but annoying misprint: Fm should, after the signs tl and U, always read TO.