An alternative approach to the decomposition of functions

Closed-constructible functions are piecewise closed

“…It is known, however, that if a decomposition is possible, it leads to preservation of even other Borel classes [9]. Recently, this question was fully and affirmatively resolved by Gao and Kleinfield [1], Holický and Pol [3].In the following publications [8,10] we have obtained such a decomposition into open, closed and continuous functions in the case of simplest Borel functions.In the present paper we give an affirmative solution for the first case when images of closed sets 2 are unrestricted combinations of closed and open sets. …”

“…In the following publications [8,10] we have obtained such a decomposition into open, closed and continuous functions in the case of simplest Borel functions.…”