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https://math.stackexchange.com/questions/1344706/are-continuous-functions-with-compact-support-bounded
While studying measure theory I came across the following fact: K(X) ⊂ Cb(X) (meaning the continuous functions with compact support are a subset of the bounded continuous functions). This seems somehow odd to me; I've tried to prove it but did not succeed.
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
https://www.planetmath.org/CompactlySupportedContinuousFunctionsAreDenseInLp
Since this kind of simple functions are dense in L p (X) we see that C c (X) is also dense in L p (X). Title compactly supported continuous functions are dense in L p
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
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,...
https://ocw.mit.edu/courses/mathematics/18-101-analysis-ii-fall-2005/lecture-notes/lecture14.pdf
3.9 Support and Compact Support Now for some terminology. Let U be an open set in Rn, and let f : U → R be a continuous function. Definition 3.26. The support of fis supp f= x∈ U: f(x) = 0}. (3.164) For example, supp f Q = Q. Definition 3.27. Let f : U → R be a continuous function. The function f is compactly supported if supp fis ...
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
https://en.wikipedia.org/wiki/Function_space
() continuous functions with compact support bounded functions continuous functions which vanish at infinity continuous functions that have continuous first r derivatives.
https://en.wikipedia.org/wiki/Compact_space
Properties of compact spaces Functions and compact spaces. A continuous image of a compact space is compact. This implies the extreme value theorem: a continuous real-valued function on a nonempty compact space is bounded above and attains its supremum. (Slightly more generally, this is true for an upper semicontinuous function.)
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