Tag Archives: ordinal

Localic products and Till Plewe’s game

Products in the category of locales resemble, but do not coincide with products in the category of topological spaces. Till Plewe has a nice explanation to this, as I will explain in this month’s post: the localic product of two … Continue reading

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On Till Plewe’s game and Matthew de Brecht’s non-consonance arguments

Last time I mentioned that S0 is not consonant. I will give Matthew de Brecht’s proof of that. Perhaps the most interesting part of this proof is a criterion that he proves and uses: if a space X is consonant, … Continue reading

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Aliaume Lopez’ master theorem of Noetherian spaces

There are quite a few constructions that we can use to build new Noetherian spaces from old ones: spaces of finite words, of finite trees (as in Section 9.7 of the book), and a few others. Instead of writing a new … Continue reading

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Compact scattered subsets and a topological game

Showing that Q is not consonant is quite an ordeal. I have finally managed to understand one of the existing proofs of this fact, due to Costantini and Watson. This would be a bit too long to cover entirely in … Continue reading

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Statures of Noetherian spaces I: maximal order types of wpos

I have had a very gifted masters 2 student from mid-May to late July, Bastien Laboureix. He mostly solved the questions I had left open here. I wanted to report on his work, but that is a lot too technical … Continue reading

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