Remark on the point of continuity property. II. (English) Zbl 0835.54015

Summary: We prove in particular that if \(X\) is a hereditarily Baire space which has the tightness less than the least weakly inaccessible cardinal and each (closed) subspace of \(X\) has the countable chain condition, then every Borel class one map of \(X\) into a metric space \(M\) has the point of continuity property. In the case of countable tightness the assumption that every closed subspace has the countable chain condition is not needed and we get a result of R. W. Hansell [in “Constantin Carathéodory: an international tribute, Vol. I, 461-475 (1991; Zbl 0767.54010)].


54C10 Special maps on topological spaces (open, closed, perfect, etc.)
54H05 Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)
03E35 Consistency and independence results