Author Archives: jgl

Coherence of Dcpos

Posted on April 2, 2017 by jgl

It had been a long time since I wanted to explain a nifty result by Jia, Jung, and Li (2016), which gives a simple test for whether a given well-filtered dcpo is coherent.  The proof, in particular, is extremely nifty.  … Continue reading →

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Open Problems

Posted on February 23, 2017 by jgl

There are a few questions that I would like to solve, and I’ve decided to share them with you.  See the new open problems page.  I am starting with three questions now, but I will update that from time to … Continue reading →

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Pointwise directed families of maps

Posted on January 12, 2017 by jgl

Happy New Year 2017!  Sorry I have not posted for some time…  Today, let me talk about a curious construction of Lawson and Xi on families of continuous maps that are not directed, rather pointwise directed.  They use that to … Continue reading →

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Some new, easy facts on consonant spaces

Posted on October 14, 2016 by jgl

Last time, we had stated and proved the Dolecki-Greco-Lechicki theorem: every regular Čech-complete space is consonant.  I would like to show that there are some other classes of consonant spaces, among T0 spaces.  The results are going to be easy … Continue reading →

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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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