On Jun 18, 7:26 pm, David C. Ullrich <ullr...@math.okstate.edu> wrote: > On Wed, 17 Jun 2009 08:18:52 -0700 (PDT), Mark Dickinson > >Right. Or rather, you treat it as the image of such a function, > >if you're being careful to distinguish the curve (a subset > >of R^2) from its parametrization (a continuous function > >R -> R**2). It's the parametrization that's uniformly > >continuous, not the curve, > > Again, it doesn't really matter, but since you use the phrase > "if you're being careful": In fact what you say is exactly > backwards - if you're being careful that subset of the plane > is _not_ a curve (it's sometimes called the "trace" of the curve".
Darn. So I've been getting it wrong all this time. Oh well, at least I'm not alone: "Definition 1. A simple closed curve J, also called a Jordan curve, is the image of a continuous one-to-one function from R/Z to R2. [...]" - Tom Hales, in 'Jordan's Proof of the Jordan Curve Theorem'. "We say that Gamma is a curve if it is the image in the plane or in space of an interval [a, b] of real numbers of a continuous function gamma." - Claude Tricot, 'Curves and Fractal Dimension' (Springer, 1995). Perhaps your definition of curve isn't as universal or 'official' as you seem to think it is? Mark -- http://mail.python.org/mailman/listinfo/python-list
