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https://math.stackexchange.com/questions/465216/space-of-continuous-functions-with-compact-support-dense-in-space-of-continuous
Space of continuous functions with compact support dense in space of continuous functions vanishing at infinity [closed]
https://math.stackexchange.com/questions/3432720/space-of-continuous-functions-with-compact-support-dense-in-space-of-integrable
Space of continuous functions with compact support dense in space of integrable functions [closed]
https://www.researchgate.net/publication/259260858_Continuous_functions_with_compact_support
Continuous functions with compact support 107 (4) M is Hausdorff, if and only if, for every pair of distinct maximal ideals M and N of K there exist points a, b ∈ K such that a 6∈ M , b 6∈ N
http://www.ams.org/journals/tran/1971-156-00/S0002-9947-1971-0275367-4/S0002-9947-1971-0275367-4.pdf
Gillman and Jerison have shown that when A'is a realcompact space, the functions in C(X) with compact support are precisely the functions which belong to every free maximal ideal in C(X). This result, and other general background material, may be found in our basic reference [GJ].
https://web.math.princeton.edu/~const/spa.pdf
The space of continuous functions on a compact is C(K) = ff: K!Cjfcontinuousg where KˆRn is compact. The norm is kfk= sup x2K jf(x)j. The H older class C is the space of bounded contuous functions with norm kfk C = sup x2 jf(x)j+ sup x6=y jf(x) f(y)j jx yj with 0 < <1. When = 1 we have the Lipschitz class. We will describe Sobolev classes shortly.
https://ncatlab.org/nlab/show/compact+support
Definition 0.1. A function on a topological space with values in a vector space (or really any pointed set with the basepoint called ) has compact support (or is compactly supported) if the closure of its support, the set of points where it is non-zero, is a compact subset. That is, the subset is a compact subset of . Typically,...
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