Khmyleva, T.; Sukhacheva, E. Linear homeomorphic classification of spaces of continuous functions defined on \(S_A\). (English) Zbl 1436.54024 Topology Appl. 275, Article ID 107024, 6 p. (2020). Summary: For a subset \(A\) of the real line \(\mathbb{R} \), modification of the Sorgenfrey line \(S_A\) is a topological space whose underlying points set is the reals \(\mathbb{R}\) and whose topology is defined as follows: points from \(A\) are given the neighbourhoods of the right arrow while remaining points are given the neighbourhoods of the Sorgenfrey line \(\mathbb{S} \) (or left arrow). A necessary and sufficient condition under which the space \(C_p( S_A)\) is linearly homeomorphic to \(C_p(\mathbb{S})\) is obtained. MSC: 54E52 Baire category, Baire spaces 46E10 Topological linear spaces of continuous, differentiable or analytic functions Keywords:Sorgenfrey line; condensation point; Baire space; linear homeomorphism; space of continuous functions endowed with the topology of pointwise convergence PDFBibTeX XMLCite \textit{T. Khmyleva} and \textit{E. Sukhacheva}, Topology Appl. 275, Article ID 107024, 6 p. (2020; Zbl 1436.54024) Full Text: DOI References: [1] Arhangelskii, A. V., Topological Spaces of Functions, 222 (1989), MSU: MSU Moscow, (in Russian) [2] Van Douwen, E. K., Retracts of the Sorgenfrey line, Compos. Math., 38, 2, 155-161 (1979) · Zbl 0408.54004 [3] Khmyleva, T. E.; Sukhacheva, E. S., On a homeomorphism between the Sorgenfrey line S and its modification \(S_P\), Math. Notes, 103, 1-2, 259-270 (2018) · Zbl 1408.54008 [4] Van Mill, J., The Infinite-Dimensional Topology of Function Spaces, 630 (2001), Elsevier: Elsevier Amsterdam · Zbl 0969.54003 [5] Tkachuk, V. V., A \(C_p\)-Theory Problems Book. Topological and Functions Space, 485 (2011), Springer: Springer New York · Zbl 1222.54002 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.