In the context of generalized metrizability of spaces I'm interested in the property of a topological space that every open set in it is a union of closed sets. A google search led me to: http://at.yorku.ca/cgi-bin/bbqa?forum=ask_a_topologist_2003;task=show_msg;msg=0048.0002 however, I do not have the mentioned book nor will it be likely I can get it any time soon. Specifically, it would appear the book calls such spaces $\pi_1$ spaces and it proves that a space is $\pi_1$ precisely when every principal a-ideal in the lattice of open sets is normal.
I would really like to understand this theorem. Unfortunately, I don't know what a-ideal means nor what normality for an ideal in that context is.
So, if anybody can contribute to deciphering the meaning of these concepts and/or point to an online available proof and/or supply a proof I will be very grateful.
I am also interested in the hierarchy of $\pi_i$ properties for spaces.