r/math • u/Short-Cheek2650 • 1d ago

What's a good place to learn pointless topology ?

I am looking for a text/lecture series on the theory of locales (pointless topology) . I don't want to go into much depth I just want to get a broad picture . My goal with this is to be able to understand topos theory better , as Andre Joyal in a lecture at IHES suggests that before learning topos theory it's better to have an idea of the theory of locales as there are a lot of parallels .

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u/ange1obear 1d ago

I found Johnstone's Stone Spaces very readable. The first two chapters give a pretty good sense of the broad picture, I think. But if you're only interested in them as they bear on topos theory, I'd just start with Mac Lane & Moerdijk's Sheaves in Geometry and Logic. The beginning of Chapter IX gives a quick introduction to locales, which by this point of the text are a very natural generalization of spaces that captures their essentials for sheaf-theoretic purposes.

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u/ModelSemantics 1d ago

These are the classics I came to suggest as well.

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u/Redrot Representation Theory 1d ago

Yeah Johnstone was the reference I used when I had to learn the stuff for a project. It's a bit encyclopedic, but it worked.

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u/ABranchingLine 1d ago

Don't call it pointless. You'll hurt the topologist's feelings.

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u/sentence-interruptio 1d ago

let's call it pointfree.

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u/Even-Top1058 Logic 1d ago

The standard reference these days is Frames and Locales by Picado and Pultr.

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u/MoSSkull 1d ago

Has to be said that they have a following book, separation in Point-free topology, which although is a "sequel", has a cleaner explanation of the topic than the original text.

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u/Even-Top1058 Logic 1d ago

I wasn't aware of that, thanks for bringing it to my attention.

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u/integrate_2xdx_10_13 1d ago

I enjoyed Topology Via Logic. Quite a dry humour vibe that old British textbooks used to have that takes me back.

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u/mathlyfe 22h ago

This is what I read.

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u/SlimyResearcher 1d ago

What’s the point? (pun absolutely intended)

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u/IllustriousMode808 3h ago

Why would you ever learn a pointless topology?