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Tag Archives: game
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
Posted in Uncategorized
Tagged consonance, counterexample, frame, game, locale, ordinal
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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
Posted in Uncategorized
Tagged consonance, counterexample, game, ordinal
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Q is not consonant: the Costantini-Watson argument
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
Posted in Uncategorized
Tagged compact, consonance, counterexample, game, scattered
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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
Posted in Uncategorized
Tagged compact, game, ordinal, scattered
Comments Off on Compact scattered subsets and a topological game