Vladimir V. Tkachuk
A note on splittable spaces

Comment.Math.Univ.Carolinae 33,3 (1992) 551-555.

Abstract:A space $X$ is splittable over a space $Y$ (or splits over $Y$) if for every $A\subset X$ there exists a continuous map $f:X\rightarrow Y$ with $f^{-1} f A=A$. We prove that any $n$-dimensional polyhedron splits over $\bold R^{2n}$ but not necessarily over $\bold R^{2n-2}$. It is established that if a metrizable compact $X$ splits over $\bold R^n$, then $\dim X\leq n$. An example of $n$-dimensional compact space which does not split over $\bold R^{2n}$ is given.

Keywords: splittable, polyhedron, dimension
AMS Subject Classification: 54A25