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- W4299885556 abstract "Let X be a compact Hausdorff space and M a metric space. E_0(X,M) is the set of f in C(X,M) such that there is a dense set of points x in X with f constant on some neighborhood of x. We describe some general classes of X for which E_0(X,M) is all of C(X,M). These include beta N - N, any nowhere separable LOTS, and any X such that forcing with the open subsets of X does not add reals. In the case that M is a Banach space, we discuss the properties of E_0(X,M) as a normed linear space. We also build three first countable Eberlein compact spaces, F,G,H, with various E_0 properties: For all metric M: E_0(F,M) contains only the constant functions, and E_0(G,M) = C(G,M). If M is the Hilbert cube or any infinite dimensional Banach space, E_0(H,M) is not all of C(H,M), but E_0(H,M) = C(H,M) whenever M is a subset of RR^n for some finite n." @default.
- W4299885556 created "2022-10-03" @default.
- W4299885556 creator A5022605683 @default.
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- W4299885556 date "1995-05-07" @default.
- W4299885556 modified "2023-09-28" @default.
- W4299885556 title "Locally Constant Functions" @default.
- W4299885556 doi "https://doi.org/10.48550/arxiv.math/9505204" @default.
- W4299885556 hasPublicationYear "1995" @default.
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