Decompositions of metrizable compact spaces admittingT-systems of complex-valued functions

Abstract

ABSTRACT. Upper semicontinuous decompositions into continua of a metrizable compact space admitting a Chebyshev system of continuous complex-valued functions are considered. It is proved that the cyclic elements of the Moore decomposition space can be embedded in the two-dimensional sphere.KEY WORDS: upper semicontinuous decomposition, Chebyshev system, Moore decomposition, cyclic elements, space of finite sets.