Author Archives: jgl

The Dolecki-Greco-Lechicki Theorem

Posted on August 25, 2016 by jgl

I have met Szymon Dolecki at the Summer Topology Conference 2016, and he is a charming person.  In 1995, with Gabriele Greco and Alojzy Lechicki, he proved a very nice theorem — every Čech-complete space is consonant — that deserves … Continue reading →

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Summer Topology Conference 2016

Posted on July 30, 2016 by jgl

I have already said I would be at the Galway Colloquium in Leicester, UK, on Monday, August 1st, 2016. Right after that, I will participate to the 2016 Summer Topology Conference—same place, from Tuesday to Friday. I will give a … Continue reading →

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Galway Colloquium 2016

Posted on July 5, 2016 by jgl

I will be at the Galway Colloquium at Leicester, UK, on Monday, August 1st, 2016.  I will give an introduction to T0 topology and domain theory there, aimed mostly at students in mathematics. I will try to illustrate some of … Continue reading →

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Locales, sublocales III: the frame of nuclei

Posted on June 16, 2016 by jgl

My goal today is to describe two elegant proofs of the fact that nuclei form a frame. There are many proofs of that. The main difficulty is that, while meets (infima) of nuclei are taken pointwise, joins (suprema) are much … Continue reading →

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Locales, sublocales II: sieves

Posted on May 11, 2016 by jgl

Last time, I promised you we would explore another way of defining sublocales.  We shall again use the naive approach that consists in imagining how we would encode subspaces of a T0 topological space X by looking at open subsets … Continue reading →

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Locales, sublocales I

Posted on April 10, 2016 by jgl

Stone duality leads naturally to the idea of locale theory.  Quickly said, the idea is that, instead of reasoning with topological spaces, we reason with frames.  The two concepts are not completely interchangeable, but the O ⊣ pt adjunction shows … Continue reading →

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Ideal Models III: Quasi-ideal domains

Posted on March 10, 2016 by jgl

I am a bit stubborn. In my first post on ideal domains, I thought I would be able to extend Keye Martin’s result from metric to quasi-metric spaces. I have said I had failed, but now I think I have … Continue reading →

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Remainders, bqos, and quasi-Polish spaces again

Posted on January 27, 2016 by jgl

In my first post on ideal domains, I thought I would be able to extend Keye Martin’s result from metric to quasi-metric spaces. That was more complicated than what I had thought. Along my journey, I (re)discovered a few results, … Continue reading →

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Ideal models II

Posted on January 3, 2016 by jgl

Last time, we have seen that every completely metrizable space X has an ideal model, that is, that X can be embedded into an ideal domain Y in such a way that we can equate X with the subspace of … Continue reading →

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Happy New Year 2016!

Posted on December 31, 2015 by jgl

I had not posted a crossword puzzle for a long time, so here is one at last: in pdf format, or in AcrossLite format, as usual.  Happy New Year!

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