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Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.

4 votes
0 answers
447 views

Why does it seem that $rca=rba$? [closed]

The following paradox has got me stumped. I'm hoping someone can point out the error. Take a locally compact metric space $X$ and define the $C_b(X)$ and $C_0(X)$ as the spaces of continuous real-val …
3 votes
2 answers
934 views

Reference for proof that $C_b^* = rba$

The following theorem seems to have folk status: The topological dual of the space $C_b(X)$ of bounded continuous functions on a topological space $X$ is isomorphic to the space $rba(X)$ of finite, r …