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Linear homeomorphic classification of spaces of continuous functions defined on \(S_A\). (English) Zbl 1436.54024

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
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References:

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