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Advice on constructing a sequence of functions when proving a set is not closed.

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#functional-analysis #advice #sequence-of-function
61
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Convergence of sequence of functions with supremum metric

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#uniform-convergence #sequence-of-function
71
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convergence of series of sinus functions

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#real-analysis #functional-analysis #uniform-convergence #sequence-of-function
24
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The limit is positive is the sequence bounded uniformly?

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#functional-analysis #ordinary-differential-equations #sequence-of-function
284
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Is the pointwise limit of monotonically increasing functions a uniform limit?

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#real-analysis #sequences-and-series #sequence-of-function
108
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$f_n(x) = (n+1)x^n(1-x)$, on which interval does $f_n$ converge uniformly?

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#real-analysis #uniform-convergence #sequence-of-function
121
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Find the pointwise limit of the sequence$f_n(x) = {1\over 1+x} + {2\over 1+x^2} + {4\over 1+x^4}+...+{2^n\over 1+x^{2^n}}$

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#real-analysis #uniform-convergence #sequence-of-function #pointwise-convergence
37
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Find a sequence of continuous functions that converges to a piecewise function

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#real-analysis #sequences-and-series #continuity #sequence-of-function
81
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Uniform convergence of telescopic function series

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#real-analysis #uniform-convergence #sequence-of-function
372
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pointwise convergence does not imply uniform convergence for series

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#real-analysis #uniform-convergence #sequence-of-function #pointwise-convergence
566
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$f_n(x)= f(x+n)$ show that the limit function is uniformly continuous

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#sequences-and-series #continuity #uniform-convergence #uniform-continuity #sequence-of-function
55
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differentiable and sequences of functions

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#real-analysis #calculus #ordinary-differential-equations #analysis #sequence-of-function
94
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uniform convergence of $f_n(x)=1/n^x$

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#real-analysis #sequence-of-function
197
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Uniform convergence in $[0,1]$

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#sequences-and-series #analysis #metric-spaces #uniform-convergence #sequence-of-function
68
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Limit of a sequence of functions of a sequence of reals

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#real-analysis #sequences-and-series #sequence-of-function

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