[FOM] constructive Tychonov

[Andrej Bauer]

Robert Black wrote:
> I ask because it seems to me that using classical Tychonov with the 
> usual definition of compactness as open covers having finite 
> subcovers it's rather straightforward to get the fan theorem

Sorry, I missed this part. I belive Troelstra and van Dalen's
"Constructivism in Mathematics" will have a bit to say, but possibly
more relevant is:

D. Bridges, H. Ishihara, P. Schuster: ‘Compactness and continuity,
constructively revisited’, in: Computer Science Logic (J. Bradfield, ed;
Proceedings of 16th International Workshop CSL 2002, 11th Annual
Conference of the EACSL, Edinburgh, Scotland, September 22–25), Lecture
Notes in Computer Science 2471, 89–102, Springer–Verlag, Berlin and
Heidelberg, 2002.

H. Ishihara, P. Schuster: Compactness under constructive scrutiny, MLQ
Math. Log. Q. 50 (2004), 540-550.

I can't find electronic version online, except those offered by evil
publishers who want more money for something that was already payed for
by public money.

Best regards,

Andrej Bauer