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On axial functions
- Speaker(s)
- Marcin Szyszkowski
- Affiliation
- Uniwersytet Gdański
- Date
- Nov. 5, 2014, 4:15 p.m.
- Room
- room 5050
- Seminar
- Topology and Set Theory Seminar
A function f : X × Y → X × Y is axial if it is of one of two types:
f(x, y) = (g(x, y), y) for some g : X × Y → X or f(x, y) = (x, g(x, y)) for
some g : X × Y → Y .
We show which functions (from the plane to the plane) are compositions
of finitely many axial functions answering some problems of Ulam.
E.g. every function is a composition of only three axial functions. But there are continuous functions that can not be even approximated by compositions of continuous axial functions. Borel functions, however, can be written as compositions of axial Borel functions.
f(x, y) = (g(x, y), y) for some g : X × Y → X or f(x, y) = (x, g(x, y)) for
some g : X × Y → Y .
We show which functions (from the plane to the plane) are compositions
of finitely many axial functions answering some problems of Ulam.
E.g. every function is a composition of only three axial functions. But there are continuous functions that can not be even approximated by compositions of continuous axial functions. Borel functions, however, can be written as compositions of axial Borel functions.
