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1. • CommentRowNumber1.
   • CommentAuthorPieter
   • CommentTimeJun 9th 2019
   • PermaLink
   Author: Pieter
   Format: MarkdownItexHi 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

   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

2. • CommentRowNumber2.
   • CommentAuthorPieter
   • CommentTimeJun 9th 2019
   • PermaLink
   Author: Pieter
   Format: MarkdownItexHm, 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...

   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…