Let (x,d) be a metric space. Let {xn} be a sequence in x: When do you say (x,d) is compact? f) What is the statement of Borel theorem that characterize compact subset of R^*. g) Let Fn : D ⊆ R, F : D -> R. When do you say that Fn converges uniformly to F on D? h) Give an example if F : (0,1) -> R that is bounded and continuous but not uniformly continuous on (0,1).

Let (x,d) be a metric space. Let {xn} be a sequence in x: When do you say (x,d) is compact? f) What is the statement of Borel theorem that characterize compact subset of R^*. g) Let Fn : D ⊆ R, F : D -> R. When do you say that Fn converges uniformly to F on D? h) Give an example if F : (0,1) -> R that is bounded and continuous but not uniformly continuous on (0,1).

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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