On Topological Classification of Function Spaces C p (X) of Low Borel Complexity

Recent classification and characterization results in geometric topology

“…Recall that the first Borel class consists of the absolute Here C*(X) is the subspace of C p (X) consisting of all bounded functions. Details will appear in [17]. Since for every countable metric space X the function space C (X) is in ^a ô , this theorem generalizes results of van Mill [22], Baars et al [5], and Dobrowolski et al [16].…”

Applying coordinate products to the topological identification of normed spaces

“…Define g : U -> X by g(x) = í)(x,e(/(x))). By (14) and (15), g is 2^-close to / and takes values in V. In turn, (5) and (12)implythat g takes values in W(X¡, *,) and satisfies g_1(KfW(Y,-, *,-)) = Lnu.…”

“…)-universality property of an arbitrary normed coordinate product pair (nc En, Y,c H") provided each element of (JF, 2C) admits a relative closed embedding into every (En, Hf) (see Proposition 3.1). A version of 3.1 for cartesian products was earlier applied [11,13,12] in order to identify some function and sequence spaces that are homeomorphic to Q.2 = X°° . Applying 3.1 (and its variations), we show that several absolute FCT(5-spaces that underlie a "product" structure are homeomorphic to Cl2.…”

Two properties of Cp(X) weaker than the Fréchet Urysohn property

“…Then F is a free filter on Y . Since C p (X) is analytic, F is an analytic set of 2 Y , see the proof of Corollary 3.6 in [3]. Recall that every analytic space has the Baire property [10, p. …”