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• CommentRowNumber1.
• CommentAuthorPieter
• CommentTimeJun 9th 2019

Hi all,

does anyone know of situations in which Heyting-algebra homomorhpisms “work out nicely” as a type of continuous maps in topology?

I remember reading somewhere that “in a Td-seperable space, Heyting-algebra homomorphism are precisely the closed continuous functions”, but I cannot find where I read that anymore… Not even sure that it is true, since if it were, I suspect it would pop-up more often. Before trying to prove it myself, I thought it would be good to ask around ;-) If you have any other suggestions, characterizing Heyting-algebra homomorphisms in topological terms under special situations, those might help out as well.

Thanks for any pointers!

Pieter

• CommentRowNumber2.
• CommentAuthorPieter
• CommentTimeJun 9th 2019

Hm, browsing around a bit more I found it mentioned in Picado and Pultr that it is actually the open continuous functions that, under Td, preserve the Heyting operator, not the closed ones. No wonder I couldn’t find the reference at first ;-) Sorry for bothering you…

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