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Continuum theory, point-set topology, spaces with algebraic structure, foundations, dimension theory, local and global properties.

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Dense sets in the space of continuous functions

Let $X$ be a compact metric space, and let $C(X)$ be the Banach space of continuous real-valued function on $X$, with the maximum norm. Suppose $S\subset C(X)$ is a set of functions with the follow …
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