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Oct 25 at 22:17 comment added Zhen Lin A geometric morphism (of toposes) can be factorised as a surjective geometric morphism followed by a subtopos embedding, and there is a notion of dense subtopos, so in principle the answer is yes... but I would say that this probably doesn't work as hoped for "big" toposes. The reason is that any object in a topos is automatically open when taking the point of view that toposes are generalised locales.
Oct 25 at 14:08 comment added R. van Dobben de Bruyn How is this supposed to compare with the complex topology? Isn't a map of complex algebraic varieties dense in the classical topology if and only if it is dominant? Can't you use that as a definition?
Oct 25 at 11:00 history asked David Corwin CC BY-SA 4.0