It is proved that: If X is a paracompact Hausdorff space and E is a Frechet lattice then (X, E) has the separation property. This is employed to extend some varies of functions that are known for spaces of Banach lattice valued functions.
ERCAN, Zafer (1997) "Extension and Separation of Vector Valued Functions," Turkish Journal of Mathematics: Vol. 21: No. 4, Article 4. Available at: https://journals.tubitak.gov.tr/math/vol21/iss4/4