Content-Type: text/shitpost

A colleague asked me to provide “choice quotes” from Thomas's dissent, which I said “might be the most Clarence Thomasy thing I've ever read”. But I think they were disappointed, because what makes it so very Clarence Thomasy is how dry and fussy it is. Here's a choice quote, if you can call it that, which examplifies what I had in mind:

The Oklahoma Court of Criminal Appeals concluded that petitioner’s claim was procedurally barred under state law because it was “not raised previously on direct appeal” and thus was “waived for further review.” This state procedural bar was applied independent of any federal law, and it is adequate to support the decision below. We therefore lack jurisdiction to disturb the state court’s judgment.

Maybe I should write a longer article on the real blog explaining what this means. I wouldn't have to worry that doing so would kill the joke, because there is no joke and there was nothing funny to begin with.

Am I the only person who imagines that Clarence Thomas is severely constipated, like, almost all the time?

I thought that the recent McGirt decision would have some connection with _Sherrill v. Oneida Nation, but no, there is no mention of it whatever. I must be seriously confused about something, can anyone tell me what?

On review, I see that it did come up briefly in oral argument:

Sherrill is always in the room when the states and the tribes are negotiating agreements

so I'm not completely confused.

I would like to understand this better.

Finite sets are always compact. Suppose we have an infinite compact space. Is it possible that the only compact proper subspaces that it possesses are the finite ones? The answer turns out to be no. Every infinite compact space has an infinite compact proper subspace. So by repetition, every infinite compact space has an infinite descending chain of compact subspaces.

I thought hey, here we have a partial order (of infinite compact subspaces) in which every descending chain has a lower bound, so we can apply Zorn's lemma… except no, not every chain has a lower bound, what was I thinking? If we include the finite subspaces then every chain does have a lower bound and we can apply Zorn's lemma, but the result is the empty subspace so that was not useful.

Interesting: The example of !![0,1]!! shows that you can't always obtain a smaller compact subspace by deleting a finite set from the original space.

The compact subspaces of an infinite compact set form a rather interesting lattice structure. At the bottom are the finite subsets, arranged like a very ordinary Boolean lattice, but with no maximum element. (Isn't there a name for a complete associative lattice that may or may not have a maximum element?) Floating above this are the infinite compact subspaces, in which there are no minimal elements, and the original space at the top.

Consider just a relatively simple example. Let !!X!! be the one-point compactification of the natural numbers. That is, $$X = \Bbb N \cup {\infty}$$ where a subset !!G!! of !!X!! is open if and only if !!G!! is a finite set that does not contain !!∞!! or !!G!! is a cofinite set that does contain !!∞!!. An infinite compact subspace of !!X!! must contain !!∞!!.

Clarence Thomas's dissent in McGirt might be the most Clarence Thomasy thing I've ever read.