Tag Archives: consonance

The complete lattice Lfan (part II)

Last time, we had started to study the complete lattice Lfan, namely just N × N, with equality as ordering on the first component and the usual ordering on the second component, plus an extra bottom element ⊥, plus an … Continue reading

Posted in Uncategorized | Tagged , , , , , , | Comments Off on The complete lattice Lfan (part II)

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 , , , , , | Comments Off on Localic products and Till Plewe’s game

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 , , , | Comments Off on On Till Plewe’s game and Matthew de Brecht’s non-consonance arguments

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 , , , , | Comments Off on Q is not consonant: the Costantini-Watson argument

The Sorgenfrey line is not consonant

In Exercise 5.4.12 of the book, I ask the reader to prove that neither the space of rationals, Q, nor the Sorgenfrey line, Rℓ, is consonant. But the proofs I had in mind were much too simple-minded to stand any … Continue reading

Posted in Uncategorized | Tagged , , , | Comments Off on The Sorgenfrey line is not consonant