ON TOPOLOGICAL CLASSIFICATION OF FUNCTION SPACES Cp(X) OF LOW BOREL COMPLEXITY
نویسندگان
چکیده
We prove that if X is a countable nondiscrete completely regular space such that the function space C (X) is an absolute FaS-set, then C (X) is homeomorphic to <7°° , where a = {(x¡) e R00:*, = 0 for all but finitely many i} . As an application we answer in the negative some problems of A. V. Arhangel'skii by giving examples of countable completely regular spaces X and y such that X fails to be a 6R-space and a fc-space (and hence X is not a km-space and not a sequential space) and Y fails to be an N0-space while the function spaces C (X) and CJY) are homeomorphic to CJX) for the compact metric space X = {0} U {n~ : n = 1, 2, ... } .
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