user938272

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18 Questions

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6	Sequence of analytic functions on $U \subset \mathbb{C} $ tending locally uniformly to $ f $ implies $ f $ analytic on $U$
6	Prove that if $ f : D(0,1) \to D(0,1) $ is analytic with $ f(0) = 0 $, then $\frac{f(z)}{z} $ has a removable singularity at 0
4	Exhibit an integral domain $R$ and a non-zero non-unit element of $R$ that is not a product of irreducibles.
4	Show that the ideal $ (2, 1 + \sqrt{-7} ) $ in $ \mathbb{Z} [\sqrt{-7} ] $ is not principal
4	If two normed spaces are Lipschitz equivalent, then one if complete iff the other is

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280 Reputation

+5	Give an example of a sequence of uniformly continuous functions on $\mathbb{R}$ that converge pointwise to a non-uniformly continuous function
+5	Sequence of real valued functions converges pointwise but not uniformly to a continuous function
+5	Exhibit an integral domain $R$ and a non-zero non-unit element of $R$ that is not a product of irreducibles.
+5	Prove that if $ f : D(0,1) \to D(0,1) $ is analytic with $ f(0) = 0 $, then $\frac{f(z)}{z} $ has a removable singularity at 0

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0 ring-theory × 8	0 general-topology
0 complex-analysis × 3	0 abstract-algebra
0 linear-algebra × 3	0 analysis
0 real-analysis × 2

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