Lucas Corrêa

### Questions (315)

 21 Real Analysis. Suggestions. 8 Are spaces shaped like the digits 0, 8 and 9 homeomorphic topological spaces? 7 Topology “generated by” normal subgroups (Topological groups). 6 Solution to one-dimensional Wave Equation with Method of Characteristics 5 Book-recommendations “Profinite Groups”

### Reputation (1,513)

 +5 Uniform powerful pro-$p$ group isomorphic to $Z_{p}^{d}$ +3 A powerful $2$-generated $p$-group is metacyclic +3 Properties of powerfully embedded subgroups +5 Let $\sigma \in Aut(K)$ have infinite order and $F = \mathcal{F}(\sigma)$. Show that if $K/F$ is algebraic, then $K$ is normal over $F$.

 4 Let $f:\Bbb{R}^n\to \Bbb{R}$ be differentiable. Prove that $f$ is linear and show that $f(0)=0$ 4 Completing the Cayley table given certain information 3 Showing (a +b)^2= a^2 +b^2 of commutative ring. 3 What is the equality of two functions (or maps)? 3 Prove that the function $f :\mathbb{Z}\to\mathbb{Z}$ given by $f(x) = 15x − 11$ does not map onto its codomain.

### Tags (120)

 18 real-analysis × 199 6 analysis × 4 11 functions × 5 5 group-theory × 30 9 abstract-algebra × 81 5 linear-algebra × 14 7 elementary-set-theory × 3 5 multivariable-calculus × 9 6 calculus × 5 4 finite-groups × 5

### Accounts (6)

 Mathematics 1,513 rep 11 gold badge55 silver badges2121 bronze badges TeX - LaTeX 108 rep 44 bronze badges Physics 101 rep 22 bronze badges Portuguese Language 101 rep 11 bronze badge English Language Learners 101 rep 11 bronze badge