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Uniform Limit Theorem
In mathematics, the uniform limit theorem states that the uniform limit of any sequence of continuous functions is continuous. Statement More precisely, let ''X'' be a topological space, let ''Y'' be a metric space, and let ƒ''n'' : ''X'' → ''Y'' be a sequence of functions converging uniformly to a function ƒ : ''X'' → ''Y''. According to the uniform limit theorem, if each of the functions ƒ''n'' is continuous, then the limit ƒ must be continuous as well. This theorem does not hold if uniform convergence is replaced by pointwise convergence. For example, let ƒ''n'' : , 1nbsp;→ R be the sequence of functions ƒ''n''(''x'') = ''xn''. Then each function ƒ''n'' is continuous, but the sequence converges pointwise to the discontinuous function ƒ that is zero on , 1) but has ƒ(1) = 1. Another example is shown in the adjacent image. In te ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Drini Nonuniformconvergence SVG
The Drin (; sq, Drin or ; mk, Дрим, Drim ) is a river in Southern Europe, Southern and Southeastern Europe with two distributary, distributaries one discharging into the Adriatic Sea and the other one into the Bojana (river), Buna River. Its drainage basin, catchment area extends across Albania, Kosovo, Serbia, Greece, Montenegro and North Macedonia. The river and its tributaries form the Gulf of Drin, an ocean basin that encompasses the northern Albanian Adriatic Sea Coast. At long, the Drin is the Rivers of Albania, longest river of Albania of which passes across Albania and the remainder through Kosovo and North Macedonia. It starts at the Source (river), confluence of its two headwaters, namely the Black Drin and White Drin. It originates in the mountainous Northern Mountain Range (Albania), northern mountain range, flows westwards through the Albanian Alps and Dukagjin highlands, Dukagjin Highlands, and eventually drains into the Adriatic Sea, between Shëngjin an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
