Tag Archives: game

Localic products and Till Plewe’s game

Posted on March 20, 2023 by jgl

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

Posted on February 20, 2023 by jgl

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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Q is not consonant: the Costantini-Watson argument

Posted on June 20, 2022 by jgl

I have already given an argument for the non-consonance of the Sorgenfrey line Rℓ here. I would now like to explain why the space Q of rational numbers is not consonant either. That is quite a challenge. The most easily … Continue reading →

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Compact scattered subsets and a topological game

Posted on May 20, 2022 by jgl

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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