We prove that δ-derivations of a simple finite-dimensional Lie algebra over field characteristic zero, with values in module, are either inner derivations, or, the case adjoint multiplications by scalar, or some exceptional cases related to sl(2). This can be viewed as an extension classical first Whitehead Lemma.

Inspired to some researches of A. N. Whitehead, we propose an approach to pointfree geometry based on the notions of “region” and of “graded inclusion” between regions.