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% (defun c () (interactive) (find-zsh "cd ~/LATEX/ && ~/dednat4/dednat41 2008gf.tex && latex    2008gf.tex"))
% (defun c () (interactive) (find-zsh "cd ~/LATEX/ && ~/dednat4/dednat41 2008gf.tex && pdflatex 2008gf.tex"))
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\documentclass[oneside]{book}
\usepackage[latin1]{inputenc}
\usepackage{edrx08}       % (find-dn4ex "edrx08.sty")
%L process "edrx08.sty"  -- (find-dn4ex "edrx08.sty")
\input edrxheadfoot.tex   % (find-dn4ex "edrxheadfoot.tex")
\begin{document}

\input 2008gf.dnt

%*
% (eedn4-51-bounded)

Notes on GF's blog etc etc.

\bsk

Index of the slides:
\msk
% To update the list of slides uncomment this line:
%\makelos{tmp.los}
% then rerun LaTeX on this file, and insert the contents of "tmp.los"
% below, by hand (i.e., with "insert-file"):
% (find-fline "tmp.los")
% (insert-file "tmp.los")

% «.grtop-1»	(to "grtop-1")
\newpage

% --------------------
% «grtop-1»  (to ".grtop-1")
% (s "Notes on ``Grothendieck Topologies - Part I (Pretopologies)''" "grtop-1")
\myslide {Notes on ``Grothendieck Topologies - Part I (Pretopologies)''} {grtop-1}

% http://catsinthejungle.wordpress.com/2008/11/10/grothendieck-topologies-part-i-pretopologies/

http://catsinthejungle.wordpress.com/2008/11/10/

grothendieck-topologies-part-i-pretopologies/

\msk

(i) The family $\{U\}$ covers $U$.

(ii) If the family $\calU = (U_\aa)_{\aaİA}$ covers $U$ and $V \subseteq U$,

then the family $(VÌU_\aa)_{\aaİA}$ covers $V$.

(iii) If the family $\calU = (U_\aa)_{\aaİA}$ covers $U$

and for each $U_\aa İ \calU$

the family $\calV_\aa = (V_{\aa\bb})_{\bbİB_\aa}$ covers $U_\aa$

then the family $(V_{\aa\bb})_{\aaİA, \bbİB_\aa}$ covers $U$.

\msk

(i) The family $\{I_U:U \to U\}$ $P$-covers $U$.

(ii) If the family $\calU = (U_\aa \to U)_{\aaİA}$ $P$-covers $U$ and $f:V \to U$,

then the family $(V ×_U U_\aa \to V)_{\aaİA}$ $P$-covers $V$.

(iii) If the family $\calU = (U_\aa \to U)_{\aaİA}$ $P$-covers $U$

and for each $(U_\aa \to U) İ \calU$

the family $\calV_\aa = (V_{\aa\bb} \to U_\aa)_{\bbİB_\aa}$ $P$-covers $U_\aa$

then the family $(V_{\aa\bb} \to U_\aa \to U)_{\aaİA, \bbİB_\aa}$ $P$-covers $U$.





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\end{document}

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