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

Mikhail Patrakeev

paper

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

arXiv:2004.10775

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.