Abstract
Answering a question of E. K. van Douwen and W. F. Pfeffer [1], we prove that the countable power of the Sorgenfrey line is a D-space. To establish this result we use a method of proof which we call reverse induction. This method allows to establish certain properties of a product \(\prod_{{i}=0}^{\infty}{X}_{i}\) by making a kind of ``reverse induction step'' from \(\prod_{{i}={n}+1}^{\infty}{X}_{i} {\rm to} \prod_{{i}={n}}^{\infty}{X}_{i}\) for an arbitrary natural n.
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The work was performed as part of research conducted in the Ural Mathematical Center with the financial support of the Ministry of Education and Science of the Russian Federation (Agreement number 075-02-2021-1383).
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Patrakeev, M. Reverse induction proof of D property of the countable power of the Sorgenfrey line. Acta Math. Hungar. 165, 112–133 (2021). https://doi.org/10.1007/s10474-021-01169-z
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DOI: https://doi.org/10.1007/s10474-021-01169-z