Posted by J. Holmer on October 30, 2007, 12:42 pm, in reply to "Uniform Density" If the setting is C(X), "uniformly dense" means a collection E of continuous functions on X such that E is dense in C(X) with respect to the sup norm (the norm on C(X)). So the word "uniformly" is just added to emphasize that we are working with the sup norm. Perhaps the fear is that by just writing "dense", the interpretation would be that the set E is dense with respect to the L^2(X) norm or some other topology on the space of functions.
Board Administrator
The meaning of uniformly dense depends upon the context.
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