Geodesic
A note on splittable spaces
Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992) no. 3, pp. 551-555 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 54A25, 54D99
Keywords: splittable; polyhedron; dimension 
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Tkachuk, Vladimir V. A note on splittable spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992) no. 3, pp. 551-555. http://geodesic.mathdoc.fr/item/CMUC_1992_33_3_a16/

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