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

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.