Decompositions of metrizable compact spaces admitting \(T\)-systems of complex-valued functions (Q1277519)

Let \(C(Q,\mathbb{C})\) be the space of continuous complex-valued functions on the space \(Q\). Let \(Q\) be the metrizable compact space and \(C(Q,\mathbb{C})\) contains a system of linearly independent functions \(\{f_1(q),\dots, f_n(q)\}\) such that complex polynomials on this system have the uniqueness property for elements of best approximation to any function from \(C(Q,\mathbb{C})\) (\(T(n,\mathbb{C})\)-system). The author has established the necessary condition for the existence of a \(T(n,\mathbb{C})\)-system), \(n>2\), on a continuum \(Q\) (Theorem 4). As a corollary of this it is proved that the cyclic elements of the Moore decomposition space can be embedded in the two-dimensional sphere.