О топологической разложимости невырожденных сепарабельных пространств с внутренним произведением

Collection of vectors in inner product space (IPS) we call $antineutral$ if each vector of this collection is not neutral. Antineutral system $\varsigma = \{g\}_{n \in \mathbb{N}}$ we call $step-nondegenerated$ if Lin$\{g_i | i \in \overline{1,n}\}$ (Lin X is linear hull of X) is nondegenerated for every $n \in \mathbb{N}$. In this article we proved that every nondegenerated algebraically separable lineal in IPS contains step-nondegenerated Hamel basis. In particular, this result implies existing of topological orthonormal basis in every nondegenerated separable IPS.