Independent subbases and non-redundant codings of separable metrizable spaces

The notion of an independent subbase was introduced by H. Tsuiki to apply non-redundant ω{0,1,⊥}-code representations to topological spaces. We prove that every dense in itself, separable, metrizable space X has an independent subbase and, if in addition, then X has an independent subbase of dimension n. We also study other properties of subbases related to non-redundant ω{0,1,⊥}-codings.