Holomorphic extension in holomorphic fiber bundles with (1,0)-compactifiable fiber

We use the Leray spectral sequence for the sheaf cohomology groups with compact supports to obtain a vanishing result. The stalks of sheaves R-center dot phi O-i for the structure sheaf O on the total space of a holomorphic fiber bundle phi has canonical topology structures. Using the standard Cech argument we prove a density lemma for QDFS-topology on this stalks. In particular, we obtain a vanishing result for holomorphic fiber bundles with Stein fibers. Using Kunnet formulas, properties of an inductive topology (with respect to the pair of spaces) on the stalks of the sheaf R-center dot phi O-i and a cohomological criterion for the Hartogs phenomenon we obtain the main result on the Hartogs phenomenon for the total space of holomorphic fiber bundles with (1, 0)-compactifiable fibers.