On Sierpinski-Zygmund bijections and their inverses


Krzysztof Ciesielski and Tomasz Natkaniec

Topology Proc. 22 (1998), 155-164.

In the paper we will examine when the inverses of one-to-one Sierpinski-Zygmund partial functions from R to R are also of Sierpinski-Zygmund type. We show that the existence of a partial Sierpinski-Zygmund function f with f-1 being also Sierpinski-Zygmund is independent of ZFC axioms of set theory. However, there exists a one-to-one Sierpinski-Zygmund injection f:R-->R such that f-1 is not Sierpinski-Zygmund. This work is related to the investigation of algebraic properties of the Sierpinski-Zygmund functions discussed in K. Ciesielski, T. Natkaniec, Algebraic properties of the class of Sierpinski-Zygmund functions.

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Last modified January 11, 1999.