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 Feb 4 comment Riesz representation for an infinite-dimensional space I looked up projective limit, but I don't see why $C(X)$ is the projective limit of $C(K)$. Would you please indicate what are the coordinate spaces and the bonding maps in the inverse limit? Feb 4 awarded Commentator Feb 4 comment Riesz representation for an infinite-dimensional space According to my topology book, there is a restriction. The statement, "a function on X is continuous iff its restrictions on compact subsets are continuous" requires X to be compactly generated. However, in my case X is compactly generated. Feb 4 comment Riesz representation for an infinite-dimensional space @Yemon, which smaller space do you suggest to consider instead of $C(X)$? Do you know of a reference for Riesz representation for $C(X)$ where $X$ is a metrizable non LCH space? Feb 4 comment Riesz representation for an infinite-dimensional space What does it mean that $C(X)$ is the projective limit of $C(K)$? Does this require X to be a countable union of compact sets? Feb 4 comment Riesz representation for an infinite-dimensional space @Yemon, You are misunderstanding the question. I give you a Banach algebra $X$ that is infinite dimensional. I am asking for a topology on $C(X)$ and a characterization of its dual. I am asking if anyone has seen such sort of theorem. The focus is the infinite-dimensionality of $X$. Either you have seen a Riesz-type theorem for infinite-dimensional spaces or not. If you don't like $X$ being an algebra, assume it's just a Banach space, or assume it's just a topological vector space. Feb 3 comment Riesz representation for an infinite-dimensional space $C(X)$ can be given a topology (most likely not a normable), but I don't want to specify one because that is part of the question. I am asking if there is some sort of Riesz representation theorem for an infinite-dimensional space $X$ where $C(X)$ has some nontrivial topology? Feb 3 comment Riesz representation for an infinite-dimensional space Is $C(X)$ suppose to be a Banach space? Feb 3 comment Riesz representation for an infinite-dimensional space I didn't say $C(X)$ is a Banach space. Feb 3 asked Riesz representation for an infinite-dimensional space Dec 4 comment Absolutely Continuous Invariant Measures for Piecewise Convex Maps You can get away with $C^{1+\alpha}$, but with less regularity, I'm not sure. Dec 3 awarded Editor Dec 3 revised Absolutely Continuous Invariant Measures for Piecewise Convex Maps added 341 characters in body Dec 3 answered Absolutely Continuous Invariant Measures for Piecewise Convex Maps Oct 26 answered Applications of Hilbert's metric Oct 19 awarded Supporter Sep 17 awarded Student Sep 15 awarded Teacher Sep 14 answered Fundamental Examples Jun 22 awarded Enthusiast