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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
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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.
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