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Tag Archives: uniform convergence
Basic Analysis: Closed Subsets and Uniform Continuity
Let’s consider another question: suppose f : D → R is continuous, where D is a subset of R. If (xn) is a sequence in D converging to some real L, is it true that (f(xn)) is also convergent? Now if L is in D, then we know that (f(xn)) → (f(L)). … Continue reading
Posted in Notes
Tagged advanced, analysis, closed subsets, continuity, points of accumulation, uniform continuity, uniform convergence
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Basic Analysis: Uniform Convergence
Once again, let be a subset. Suppose we now have a sequence of functions , where n = 1, 2, 3, … , such that for each x in D, the sequence converges to some real value. We’ll denote this value by f(x), thus … Continue reading
Posted in Notes
Tagged advanced, analysis, continuity, convergence, pointwise convergence, series, uniform convergence
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