Reverse induction proof of D property of the countable power of the Sorgenfrey line

Mikhail Patrakeev

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arXiv · 2004.10775

Reverse induction proof of D property of the countable power of the Sorgenfrey line

Mikhail Patrakeev

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Abstract

We present a new 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 $\prod_{{i}={n}+1}^{\infty}{X}_{i}$ to $\prod_{{i}={n}}^{\infty}{X}_{i}$ for an arbitrary natural ${n}$. Using this method we answer a question posed by E. K. van Douwen and W. F. Pfeffer in 1979 by proving that the countable power of the Sorgenfrey line is a D-space.

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Mikhail Patrakeev. 2020-04-22. Reverse induction proof of D property of the countable power of the Sorgenfrey line. https://arxiv.org/abs/2004.10775

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