A note on splittable spaces

@article{Tkachuk1992,
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 $\mathbf \{R\}^\{2n\}$ but not necessarily over $\mathbf \{R\}^\{2n-2\}$. It is established that if a metrizable compact $X$ splits over $\mathbf \{R\}^n$, then $\dim X\le n$. An example of $n$-dimensional compact space which does not split over $\mathbf \{R\}^\{2n\}$ is given.},
author = {Tkachuk, Vladimir Vladimirovich},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {splittable; polyhedron; dimension; splittability; polyhedron},
language = {eng},
number = {3},
pages = {551-555},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {A note on splittable spaces},
url = {http://eudml.org/doc/247369},
volume = {33},
year = {1992},
}

TY - JOUR
AU - Tkachuk, Vladimir Vladimirovich
TI - A note on splittable spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1992
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 33
IS - 3
SP - 551
EP - 555
AB - 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 $\mathbf {R}^{2n}$ but not necessarily over $\mathbf {R}^{2n-2}$. It is established that if a metrizable compact $X$ splits over $\mathbf {R}^n$, then $\dim X\le n$. An example of $n$-dimensional compact space which does not split over $\mathbf {R}^{2n}$ is given.
LA - eng
KW - splittable; polyhedron; dimension; splittability; polyhedron
UR - http://eudml.org/doc/247369
ER -