Supplemented spaces of the functions on the Peano continua

Abstract

A description of the topology of the pair $(\tilde {C} (\Pi, I), C (\Pi, I))$ for the Peano continuum $\Pi$, where $\tilde {C} (\Pi, I)$ is the closure in the hyperspace ${\rm ехр} (\Pi \times I)$ of the image of the space of continuous functions $C (\Pi, I)$ under the natural embedding, is obtained.