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.
Categories: math.GN math.LO
