MATHEMATICS

On a linear homeomorphism of spaces of continuous functions on subsets of the Sorgenfrey line

N. N. Trofimenko, T. E. Khmyleva

Tomsk State University

Abstract: In this paper, it is proved that the spaces $C_p(I)$ and $C_p(\mathcal E)$ are linearly homeomorphic. Here, the interval $I=[0,1]$ and a Cantor set $\mathcal E$ are equipped with the Sorgenfrey topology.

Keywords: Sorgenfrey topology, spaces of continuous functions, linear homeomorphism, complemented subspace.

UDC: 515.12

Received: 26.04.2012