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25 votes
Accepted

Suppose that $f ' (x)$ exists and $f(x)$ has two roots $x_1$ and $x_2$. Try to prove that:

16 votes
Accepted

Prove that the center of G has order divisible by p

14 votes
Accepted

Finding the norm of the shift operator on $l^\infty$, $(x_1,x_2, \dots)\mapsto (x_2,x_3,\dots)$

14 votes

Is there an elegant way to prove a function is linear?

13 votes

Metric is continuous function

9 votes
Accepted

A function continuous and bounded on a closed and bounded set but not uniformly continuous there

8 votes

How many matrices are there in the vector space $M_{m \times n} (\mathbb{Z}_2)$?

8 votes

Difference between homomorphisms and homomorphic images

8 votes
Accepted

Sum $\frac{1}{6} + \frac{5}{6\cdot 12} + \frac{5\cdot 8}{6\cdot 12\cdot 18} + \frac{5\cdot 8\cdot 11}{6\cdot 12\cdot 18\cdot 24}+\ldots$

8 votes
Accepted

Give $[0,1]^{\omega}$ the uniform topology. Find an infinite subset of this space that has no limit point.

6 votes

A subspace $X$ is closed iff $X =( X^\perp)^\perp$

6 votes

Is a continuous bijection function from a hausdorff space to a compact space a homeomorphism?

6 votes

Is that Ring a field?

6 votes

Absolute convergence to zero imply convergence to zero?

6 votes

A well defined homomorphism from $\mathbb{Z}/48\mathbb{Z}$ into $\mathbb{Z}/{36}$

6 votes
Accepted

Group Theory : What is $Ha \ne Hb$?

6 votes
Accepted

Suggestions for research in Group Theory

6 votes

Prove that the function $x\mapsto\sin(x^{2})$ is not periodic

6 votes
Accepted

Book recommendation for Lebesgue integration and Fourier Analysis

6 votes

Prove that the normalizer of the subgroup is the subgroup is itself

6 votes

Prove that $a_n=1+\frac{1}{1!} + \frac{1}{2!} +...+ \frac{1}{n!}$ converges using the Cauchy criterion

6 votes
Accepted

Number of nonsingular $2\times2$ matrices over $GF(3)$

6 votes

If a group has order $100$ and every subgroup of $G$ is normal why can't it be non-abelian?

5 votes

Is the image of a compact set under a bounded continuous function compact?

5 votes

Analysis problem: Show that$ f(x)$ is less or equal than$ g(x)$

5 votes
Accepted

Is $T$, the set of all polynomials with integer coefficients, countable?

5 votes
Accepted

Book for Functional Analysis

5 votes
Accepted

Prove/disprove: $I \cup J$ is (always) an Ideal of $R$.

5 votes

Good abstract algebra books for self study

5 votes
Accepted

$G/Z(G)$ is cyclic useful for proving groups abelian?

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