### Questions (437)

 226 Your favourite application of the Baire Category Theorem 72 Space of bounded continuous functions is complete 62 Proof of $(\mathbb{Z}/m\mathbb{Z}) \otimes_\mathbb{Z} (\mathbb{Z} / n \mathbb{Z}) \cong \mathbb{Z}/ \gcd(m,n)\mathbb{Z}$ 35 Proof that every finite dimensional normed vector space is complete 35 The homology groups of $T^2$ by Mayer-Vietoris

### Reputation (42,071)

 +10 In what sense can the Lie algebra of $GL_n(\mathbb{C})$ be "identified" with $M_n(\mathbb C)$? +10 Continuous mapping on a compact metric space is uniformly continuous +10 Homology groups of torus +10 "Every linear mapping on a finite dimensional space is continuous"

 137 Is $\mathbf{Q}(\sqrt{2}, \sqrt{3}) = \mathbf{Q}(\sqrt{2}+\sqrt{3})$? 97 Continuous mapping on a compact metric space is uniformly continuous 66 Space of bounded continuous functions is complete 63 Prove $0! = 1$ from first principles 51 Is the space $C[0,1]$ complete?

### Tags (191)

 409 general-topology × 96 160 faq × 2 352 functional-analysis × 105 150 field-theory × 16 352 real-analysis × 93 145 algebraic-topology × 116 283 abstract-algebra × 81 131 banach-spaces × 27 190 metric-spaces × 31 107 uniform-continuity × 2

### Bookmarks (447)

 467 Best Sets of Lecture Notes and Articles 436 Proofs that every mathematician should know. [closed] 260 Norms Induced by Inner Products and the Parallelogram Law 257 Too old to start math [closed] 248 Fun but serious mathematics books to gift advanced undergraduates.