Curve on a finite interval

Reference no: EM13966700

A C 1 curve is a function t f→ ( f (t ), g(t )) from R into R2 where the derivatives f 1(t ) and g1(t ) exist and are continuous for all t. Show that R2 is not a countable union of ranges of a C 1 curves. Hint: Show that the range of a C 1 curve on a finite interval is nowhere dense.

Reference no: EM13966700

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