The Stacks project

Typos

	Thanks to Andrew Kiluk

Closed subsets of Noetherian sober spaces

	Characterization as constructible subsets closed under
	specialization. Similar for open subsets.

Topology: Fix error in lemma on existence closed point

	This was noticed by Cameron Franc. Here is the email:

	Dear project developers,

	Lemma 9.5 in the chapter on topological spaces says that "every
	nonempty quasi-compact topological space has a closed point".
	This is false: consider the trivial topology on a nonempty
	space.

	One needs to assume some mild separation axiom, for instance
	that for any two distinct points there is a closed set containing
	precisely one of the two points.

	The book is great! Keep up the good work,
	-cameron franc

Topology + Morphisms: Fix error in topology lemma + fallout

	The error was in thinking that generalizations lift along any
	open map of topological spaces, which they do not. An example
	can be constructed relatively easily.

	It turns out that we never used this anywhere in the rest of the
	chapters, which is a lucky break. We fixed a comment about this
	in the chapter on morphisms of schemes to be a little more
	clear, and we added a lemma stating explicitly that
	generalizations do lift along flat morphisms of schemes.

Started tags infrastructure

	new file:   scripts/add_tags.py
	modified:   scripts/functions.py
	new file:   tags/initial_tags
	new file:   tags/tags

Short intro to section on going up and down

	modified:   algebra.tex
	modified:   topology.tex

Added obvious material on going up down and specialization

	modified:   algebra.tex
	modified:   sites.tex
	modified:   topology.tex