[FOM] constructive continuity 2

[hendrik@topoi.pooq.com]

On Fri, Feb 08, 2008 at 02:55:32AM +0100, Frank Waaldijk wrote:

> Or 
> perhaps there is some unforeseen difficulty in moving from {R} to the formal 
> interval {[0,1]}? In both cases this seems to me to warrant some further 
> thinking.

The fact that [0, 1] is a closed interval, whereas R is like an open 
interval (0, 1) is surely relevant.

What, by the way, *is* {[0, 1]}  It seems that the formal intervals and 
neighbourhoods are joins of open intervals; wherefor they'd correspond 
to open sets in R.  [0, 1] is not open.

-- hendrik