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)].

MSC:

 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

Citations:

Zbl 0835.54014; Zbl 0767.54010