onurcanbektas

### Questions (363)

 48 If the field of a vector space weren't characteristic zero, then what would change in the theory? 18 If $A$ and $B$ are positive constants, show that $\frac{A}{x-1} + \frac{B}{x-2}$ has a solution on $(1,2)$ 10 Topologically, is there a definition of differentiability that is dependent on the underlying topology, similar to continuity? 10 True or false: If $f(x)$ is continuous on $[0, 2]$ and $f(0)=f(2)$, then there exists a number $c\in [0, 1]$ such that $f(c) = f(c + 1)$. 9 What if the basis not countable, then what?

### Reputation (3,480)

 +5 Determining the linear independence of tangent vectors at a point on the manifold +5 Isn't a smooth map having rank 2 injective by the corollary of inverse function theorem? +13 Solving $u_{\epsilon \eta} = \frac{ u_\epsilon - u_\eta}{4 (\epsilon - \eta) } .$ +5 Two doors, each either trapped or safe, have signs whose truth depends on certain circumstances. Each sign reads “Both doors are safe”.

 5 The Pigeonhole Principle 3 I would like some help proving a (seemingly simple or obvious) lemma about quotient spaces of isomorphic vector spaces. 3 Recommended Book after Finite-Dimensional Vector Spaces by Halmos 3 $\mathcal{L}(V,W)$ is infinite dimensional when $V$ is finite dimensional and $W$ is infinite dimensional. 3 Prove that If $f(x)\to a$ and $f'(x) \to b$ as $x\to +\infty$, then $b = 0$

### Tags (266)

 8 linear-algebra × 104 6 pigeonhole-principle × 2 8 calculus × 32 5 linear-transformations × 52 7 real-analysis × 86 5 abstract-algebra × 22 7 derivatives × 31 5 proof-verification × 20 6 general-topology × 37 5 multivariable-calculus × 19

### Accounts (70)

 Mathematics 3,480 rep 11037 Academia 1,162 rep 21221 Science Fiction & Fantasy 835 rep 11338 Physics 768 rep 525 Travel 343 rep 17