Characteristic mapping

in topology

A continuous mapping $\chi$ from a closed $n$-dimensional ball $E^n$ into a topological Hausdorff space $X$ that is a homeomorphism on the interior $\mathrm{int}(E^n)$ of the ball. The set $e^n = \chi[\mathrm{int}(E^n)]$ is then called a cell of $X$, and $\chi$ is called the characteristic mapping of the cell $e^n$. If $X$ is a cellular space, then the cells of $X$ are defined as those cells of $X$ that form the cellular decomposition of $X$.