[FOM] continuing problems with constructive continuity?

b.spitters@cs.ru.nl b.spitters at cs.ru.nl
Tue Feb 12 16:15:55 EST 2008

Dear Frank,

As you know these issues are close to my heart.

The crucial observation is that in order to prove that a continuous morphism 
representing a uniformly continuous function f from [0,1] to (0,1] in fact 
maps into the formal open subspace (0,1] of [0,1]. This requires (some form 
of) the fan theorem. Knowing that f(x)>0 for all x in [0,1] is not enough. 
Similarly, the fan theorem is needed to prove that inf f >0.

I hope that this is enough to reconstruct the answers to the rest of your 

I am working on a paper where these and related issues are explained at 
length, but this will take some time.



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