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For questions about frames (=lattices with arbitrary joins and such that finite meets are distributive over those, such as the open sets of a topological set) and locales (the dual category to that of frames, seen as a generalization of topological spaces), as well as about pointfree (“pointless”) topology. This includes questions both of an algebraic nature about frames and of a topological nature about locales.

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"Locally compact"-ly generated topological spaces

If $X$ is locally compactly generated then $X$ is compactly generated because every locally compact space is compactly generated. So given $f:X \to Y$ a map such that $f\circ i$ is continuous for ever …
Simon Henry's user avatar
  • 42.4k
4 votes

Dissolution of a topos

I'm not aware of litterature on this, but this is something I have thought about several years ago and never ended-up using or publishing. What is below is me trying to remind myself how it works - un …
Simon Henry's user avatar
  • 42.4k
3 votes

Preimage of a sublocale by a morphism of locales: description by nucleus?

Here is I think a counter-example to the precise proposed formula in the question. Take $X= \mathbb{Q}$ with the discrete topology, with $Y = \mathbb{R}$ withe its usual topoly and the map $f:X \to Y$ …
Simon Henry's user avatar
  • 42.4k