Semi-partition or pre-partition For a given space $X$ the partition is usually defined as a collection of sets $E_i$ such that $E_i\cap E_j = \emptyset$ for $j\neq i$ and $X = \bigcup\limits_i E_i$. 
Does anybody met the name for a collection of sets $F_i$ such that $F_i\cap F_j = \emptyset$ for $j\neq i$ but 


*

*$X = \overline{\bigcup\limits_i F_i}$ if $X$ is a topological space, or

*$\mu\left(X\setminus\bigcup\limits_i F_i\right) = 0$ if $X$ is a measure space.


I guess that semipartition or a pre-partition should be the right term, but I've never met it in the literature. 

Brian M. Scott wrote:

In the topological case I'd simply call it a (pairwise) disjoint family whose union is dense in $X$; I've not seen any special term for it.
In fact, I can remember seeing it only once: such a family figures in the proof that almost countable paracompactness, a property once studied at some length by M.K. Singal, is a property of every space.

