This isn't a precise answer to either of your two questions. However, it sounds like you're interested in learning about locales, so maybe it's useful to make the following general point.
The theory of locales is often motivated as follows: often in topology (e.g. in the definition of sheaf) the points of a space are irrelevant, so we might as well abstract them away and work with open sets only. That's fine, but what possibly doesn't get said often enough is that the resulting theory is a piece of algebra.
Let me say that more exactly. A frame is a partially ordered set with finite meets and arbitrary joins, such that meets distribute over joins. Equivalently, it is a set X equipped with:
- a binary operation $\wedge: X^2 \to X$ and a constant $\top \in X$ (thought of as the top or greatest element)
- for each set I, an I-ary operation $\bigvee_I: X^I \to X$
satisfying a bunch of equations. (There's no need to mention the order relation explicitly, since it can be recovered from the rest of the structure: $x \leq y$ iff $x \wedge y = x$.) A map of frames is a map of sets commuting with all the operations. Thus, the category of frames is a category of algebras in any of several standard senses: e.g. it's monadic over the category of sets.
(It's a slightly unusual category of algebras in that it includes infinitary operations, and indeed infinitary operations of arbitrarily high arity, but still, it shares many of the good features of old friends like the categories of groups, rings, modules, etc.)
The category of locales is by definition the opposite of the category of frames.
So, this is a really literal instance of the slogan "geometry is dual to algebra".
