This article is cited in 1 paper

Linear homeomorphisms of spaces of continuous functions on long Sorgenfrey lines

N. N. Trofimenko, T. E. Khmyleva

Faculty of Mechanics and Mathematics, Tomsk State University, Tomsk, Russia

Abstract: We carry out a linear homeomorphic classification of the spaces of continuous functions on the long Sorgenfrey lines $S_\alpha$, where $\alpha$ is an arbitrary ordinal. The spaces of continuous functions are endowed with the topology of pointwise convergence and denoted by $C_p(S_\alpha)$.

Keywords: Sorgenfrey line, linear homeomorphism, segment of ordinals, regular ordinal, initial ordinal, order topology, pointwise convergence.

UDC: 515.129

Received: 09.06.2015

DOI: 10.17377/smzh.2016.57.320

 English version: Siberian Mathematical Journal, 2016, 57:3, 558–564

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