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https://en.wikipedia.org/wiki/Compact_support
Every continuous function on a compact topological space has compact support since every closed subset of a compact space is indeed compact. Essential support [ edit ] If X is a topological measure space with a Borel measure μ (such as R n , or a Lebesgue measurable subset of R n , equipped with Lebesgue measure), then one typically identifies ...
https://math.stackexchange.com/questions/3279942/topological-spaces-in-which-a-set-is-the-support-of-a-continuous-function-iff-it
An exercise of Rudin's Real and Complex Analysis says: Is it true that every compact subset of $\mathbf{R}^1$ is the support of a continuous function? If not, can you describe the class of all compact sets in $\mathbf{R}^1$ which are supports of continuous functions? Is your description valid in other topological spaces?
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/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 the pointwise addition of functions and scalar multiplication by constants.
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.ams.org/journals/tran/1971-156-00/S0002-9947-1971-0275367-4/S0002-9947-1971-0275367-4.pdf
1. Introduction. The support of a real continuous function / on a topological space A" is the closure of the set of points in Afat which/does not vanish. 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).
https://www.encyclopediaofmath.org/index.php/Function_of_compact_support
The support of is the closure of the set of points for which is different from zero . Thus one can also say that a function of compact support in is a function defined on such that its support is a closed bounded set located at a distance from the boundary of by a number greater than , where is sufficiently small.
https://www.planetmath.org/CompactlySupportedContinuousFunctionsAreDenseInLp
compactly supported continuous functions are dense in L p. ... We denote by C c (X) the space of continuous functions X → ℂ with compact support. ... can also be approximated by a compactly supported continuous function. Since this kind of simple functions are dense in L p ...
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 ...
http://www.msc.uky.edu/ken/ma570/lectures/lecture2/html/compact.htm
Lecture 2: Compact Sets and Continuous Functions 2.1 Topological Preliminaries. What does it mean for a function to be continuous? An elementary calculus course would define: Definition 1: Let and be a function. Let and . The function has limit as x approaches a if for every , there is a such that for every with , one has . This is expressed as
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