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https://math.stackexchange.com/questions/465216/space-of-continuous-functions-with-compact-support-dense-in-space-of-continuous
How can we prove that the space of continuous functions with compact support is dense in the space of continuous functions that vanish at infinity? Stack Exchange Network Stack Exchange network consists of 175 Q&A communities including Stack Overflow , the largest, most trusted online community for developers to learn, share their knowledge ...
https://en.wikipedia.org/wiki/Compact_support
The notion of closed support is usually applied to continuous functions, but the definition makes sense for arbitrary real or complex-valued functions on a topological space, and some authors do not require that f : X → R (or C) be continuous. Compact support
https://en.wikipedia.org/wiki/Continuous_functions_on_a_compact_Hausdorff_space
In mathematical analysis, and especially functional analysis, a fundamental role is played by the space of continuous functions on a compact Hausdorff space with values in the real or complex numbers. This space, denoted by C(X), is a vector space with respect to
https://math.stackexchange.com/questions/1344706/are-continuous-functions-with-compact-support-bounded
While studying measure theory I came across the following fact: $\mathcal{K}(X) \subset C_b(X)$ (meaning the continuous functions with compact support are a …
https://www.researchgate.net/publication/259260858_Continuous_functions_with_compact_support
We show, in particular, that for continuous frames, the pointfree rings of continuous functions with compact support are Noetherian if and only if the underlying set of the frame is finite; see ...
https://ncatlab.org/nlab/show/compact+support
A function f: X → V f\colon X \to V on a topological space with values in a vector space V V (or really any pointed set with the basepoint called 0 0) 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.
https://www.planetmath.org/CompactlySupportedContinuousFunctionsAreDenseInLp
Let (X, ℬ, μ) be a measure space, where X is a locally compact Hausdorff space, ... We denote by C c (X) the space of continuous functions X → ℂ with compact support. Theroem - For every 1 ... can also be approximated by a compactly supported continuous function.
https://mathoverflow.net/questions/237636/are-compactly-supported-continuous-functions-dense-in-the-continuous-functions-o
Continuous functions on $\mathbb R^d$ such that the support is a compact subset of $\overline{\Omega}$? For "nice" $\Omega$ this would be the space of continuous functions on $\Omega$ vanishing at the boundary. $\endgroup$ – Jochen Wengenroth Apr 29 '16 at 12:50
http://www.msc.uky.edu/ken/ma570/lectures/lecture2/html/compact.htm
Definition 2:The function f is said to be continuous at if On the other hand, in a first topology course, one might define: Definition 3: A topological space is a pair (X, ) where X is a set and is a collection of subsets of X (called the open sets of the topological space) such that The Union of any number of open sets is …
http://www.ams.org/journals/tran/1971-156-00/S0002-9947-1971-0275367-4/S0002-9947-1971-0275367-4.pdf
SUPPORTS OF CONTINUOUS FUNCTIONS BY MARK MANDELKERN) Abstract. Gillman and Jerison have shown that when A" is a realcompact space, every function in C(X) that belongs to all the free maximal ideals has compact support. A space with the latter property will be called fi …
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