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https://math.stackexchange.com/questions/445735/compactly-supported-continuous-function-is-uniformly-continuous
$\begingroup$ Actually this can be answered easily if it is true that a sequence of uniformly continuous functions that converge uniformly to a continuous function, then that function necessarily uniformly continuous. $\endgroup$ – Chris Cave Feb 10 '15 at 11:52
https://www.uio.no/studier/emner/matnat/math/MAT2400/v11/ContFunc.pdf
2 CHAPTER 2. SPACES OF CONTINUOUS FUNCTIONS If the underlying space X is compact, pointwise continuity and uniform continuity is the same. This means that a continuous function defined on a closed and bounded subset of Rn is always uniformly continuous. Proposition 2.1.2 Assume that X and Y are metric spaces. If X is com-
https://math.stackexchange.com/questions/2086124/continuous-with-compact-support-implies-uniform-continuity
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up. ... Continuous with compact support implies uniform continuity. Ask Question Asked 2 years, 9 months ago. ... Must a uniformly continuous function from $\mathbb{R}$ to $\mathbb{R ...
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://www.math.wisc.edu/~robbin/521dir/cont.pdf
Example 15. The function f(x) = p xis uniformly continuous on the set S= (0;1). Remark 16. This example shows that a function can be uniformly contin-uous on a set even though it does not satisfy a Lipschitz inequality on that set, i.e. the method of Theorem 8 is not the only method for proving a function uniformly continuous.
https://en.wikipedia.org/wiki/Uniform_continuity
Uniform continuity can be expressed as the condition that (the natural extension of) f is microcontinuous not only at real points in A, but at all points in its non-standard counterpart (natural extension) * A in * R. Note that there exist hyperreal-valued functions which meet this criterion but are not uniformly continuous, as well as ...
https://www.physicsforums.com/threads/uniformly-continuous-part-2.982694/
Jan 05, 2020 · Prove that if for any two sequences (xn), (yn) Which are sustained lim(yn-xn)=0 Happening The first thing I thought about doing was to prove that f is continuous using the Heine–Cantor theorem proof. But I do not know at all whether it is possible to prove with the data that I have continuous…
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