Real Algebraic and Analytic Geometry
Submission: 2010, May 9.
In general, the closure of a metric space of definable functions contains many non-definable functions. We consider the completions of metric and normed spaces of continuous and differentiable functions which are definable in an o-minimal expansion of the real numbers and study the information about the structure contained in the completions. In many cases one can even reconstruct the structure from the completions.
Mathematics Subject Classification (2000): 03C64,40A30,26B99,45E50.
Keywords and Phrases: o-minimal structure, metric closure, space of definable functions.
Full text, 9p.: dvi 41k, pdf 103k.