Of course, by means of a

Baire category argument (as seen in [8]) one can show that almost every continuous function having zeros has, actually, an uncountable amount of them.

Moreover, we call a set F nowhere dense in E provided C(E\C(F)) = C(E), that is, if C(F) does not contain a nonempty subset of the form E [intersection] w x [X.sup.[omega]], and a subset F is referred to as of first Baire category in E if F is a countable union of sets nowhere dense in E.

Then every regular [omega]-language F [subset or equal to] E is of first Baire category in E if and only if [L.sub.[alpha]](F) = 0.

Moreover, we call a set F nowhere dense in E providedC(E\C(F)) = C(E), that is, if C(F) does not contain a nonempty subset of the form E [intersection] w * [X.sup.[omega]], and a subset F is referred to as of first Baire category in E if F is a countable union of sets nowhere dense in E.

Since E is supposed to be residual in C(E), C(E) \ E is of first Baire category in C(E), and, since E is a countable intersection of regular [omega]-languages, say [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], the difference [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is a countable union of regular [omega]-languages C(E)\[F.sub.i], each of which is of first Baire category in C(E).

Since (q)-porous sets are nowhere dense, all ([sigma], q)-porous sets are of the first

Baire category. To point out the difference between (q)-porous and nowhere dense sets, note that if E [subset] Y is nowhere dense, y [member of]Y and r > 0, then there are a point z [member of] Y and a number s > 0 such that B(z,s) [subset] B(y,r) E.

A convex body is typical as soon as it enjoys a property P such that the set of all convex bodies not enjoying P is of the first

Baire category in k.

Now, joint continuity of the map follows from

Baire category theorem [10].

The latter means that the symmetric difference [U.sub.n] [DELTA][C.sub.n] is meager (i.e., is of the first

Baire category) in W.

Although we shared common interest, we have no paper in common, and I followed his work at a distance, mainly through discussions with our common friend Giulio Pianigiani, with whom, at that time, he was developing the

Baire Category approach.

is a [G.sub.[delta] dense set by

Baire Category Theorem.

Since B is of the second

Baire category and the sets ([[Z.sup.n],.sub.m] [intersection] B) are closed, one of these sets would have a nonempty interior.