Preservation of the Borel class under open-LC functions

Alexey Ostrovsky
2011 Fundamenta Mathematicae  
Let X be a Borel subset of the Cantor set C of additive or multiplicative class α, and f : X → Y be a continuous function onto Y ⊂ C with compact preimages of points. If the image f (U ) of every clopen set U is the intersection of an open and a closed set, then Y is a Borel set of the same class α. This result generalizes similar results for open and closed functions. 2010 Mathematics Subject Classification: Primary 54C10; Secondary 54H05, 54E40, 03E15.
doi:10.4064/fm213-2-4 fatcat:27scr6xcqrbtdl3m7p6q7g5tru