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Tag Archives: scattered
Skula spaces II: the Dow-Watson counterexample
Last time, we have started to explain some results due to A. Dow and S. Watson, and we have seen that every compact T0 scattered space of scattering height at most 3 is Skula, namely can be obtained from a … Continue reading
Posted in Uncategorized
Tagged scattered, skula topology
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Skula spaces I: clopen selectors
A Skula space is a space that is obtained from another space X by giving it the Skula topology instead, which is generated by the open sets and the closed sets of the original space X. In 1990, Alan Dow … Continue reading
Posted in Uncategorized
Tagged compactness, connectedness, noetherian, scattered, skula topology
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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
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