Suppose we have a CW-complex $X$ with a 0-cell $e^0$. Is union of all the cells (of higher dimetntions) for which $e^0$ is boundary point is open in $X$?

I don't know if it has a name but similar thing for verticies of a polyhedron in russian literature is called "star"

Suppose we have a CW-complex $X$ with a 0-cell $e^0$. Is the union of all the cells (of higher dimensions) for which $e^0$ is a boundary point open in $X$?

I don't know if it has a name, but a similar thing for vertices of a polyhedron in the Russian literature is called "star".