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A space $X$ is functionally countable (FC) if for every continuous $f:X\to ℝ$, $\left|f\right(X\left)\right|\le \omega$. The class of FC spaces includes ordinals, some trees, compact scattered spaces, Lindelöf P-spaces, $\sigma$-products in $2^{\kappa }$, and some L-spaces. We consider the following three versions of functional separability: $X$ is 1-FS if it has a dense FC subspace; $X$ is 2-FS if there is a dense subspace $Y\subset X$ such that for every continuous $f:X\to ℝ$, $\left|f\right(Y\left)\right|\le \omega$; $X$ is 3-FS if for every continuous $f:X\to ℝ$, there is a dense subspace $Y\subset X$ such that $\left|f\right(Y\left)\right|\le \omega$. We give examples distinguishing...

In questo lavoro daremo una construzione che aumenta il numero di sottospazi chiusi e discreti dello spazio e daremo alcune applicazioni di tale construzione.