User user160110

31 votes

6 answers

3k views

Is every open set the interior of a closed set?

asked Feb 5, 2017 at 5:54

20 votes

4 answers

4k views

Why are subsets of compact sets not compact?

asked Feb 12, 2019 at 18:38

9 votes

0 answers

576 views

Proving $\lim\limits_{n\to \infty}\int\limits_{0}^{1} f_n(x)dx=0$

asked Dec 15, 2016 at 6:11

7 votes

1 answer

213 views

Showing a polynomial is irreducible in $\mathbb{Q}[x]$

asked Sep 2, 2017 at 18:07

6 votes

2 answers

745 views

Is $f(x)=\mu(V+x)$ continuous?

asked Jan 9, 2017 at 9:38

6 votes

1 answer

4k views

$x^p-a$ irreducible?

asked Jan 15, 2017 at 1:51

6 votes

1 answer

632 views

If $G$ is a $p$-group then $\Phi(G)=G'G^p$

asked Sep 18, 2015 at 21:36

6 votes

1 answer

6k views

Composition of a continuous function and a discontinuous function, can be continous.

asked Feb 14, 2016 at 21:57

5 votes

0 answers

127 views

Importance of compactness in Rudin problem.

asked May 26, 2015 at 18:31

4 votes

4 answers

110 views

Let $H,K\lhd G$, if $H\cong K$ and $H\cap K\neq\{1\}$ then does it follow that $H=K?$

asked Aug 15, 2015 at 13:03

4 votes

3 answers

73 views

If $K\lhd G$ and $(|K|,[G:K])=1$ then $K$ is characteristic.

asked Aug 15, 2015 at 14:37

4 votes

1 answer

213 views

Find all functions $\Phi$ on $[0,\infty)$ where $\Phi(\lim\limits_{p\to 0}||f||_p)=\int\limits_{0}^{1}(\Phi \circ f)d\mu$.

asked May 25, 2017 at 9:02

4 votes

3 answers

93 views

How would you go about writing $1/3=\sum\limits_{n=-k}^{\infty}a_n 2^{n}$ where $a_n=0,1$

asked Dec 4, 2016 at 1:40

4 votes

2 answers

733 views

Anyone Understand how the chain rule was applied here?

asked Oct 17, 2016 at 0:37

4 votes

1 answer

173 views

When does $L^r(\mu)=L^s(\mu)$?

asked Aug 9, 2017 at 18:15

4 votes

2 answers

91 views

Linearity of Uniformly Continuous functions

asked Jul 5, 2022 at 2:11

3 votes

2 answers

49 views

Understanding $\log p/q = \sum_{k=1}^{\infty} \frac{1}{2k-1}(\frac{p-q}{p+q})^{2k-1}$

asked Sep 6, 2021 at 19:32

3 votes

1 answer

74 views

Generating a countable mutually disjoint collection of arbitarally small measurable sets.

asked Aug 10, 2017 at 5:33

3 votes

2 answers

2k views

All analytic functions are constant?

asked Sep 26, 2017 at 0:18

3 votes

1 answer

53 views

Is $0\in (\bigcap\limits_{n=3}^{\infty}([0,1]-[1/n,1-1/n]))$

asked Jun 19, 2016 at 2:50

3 votes

3 answers

115 views

If a group $ G$ is not simple does it follow that it is isomorphic to the direct product of two nontrivial groups?

asked Aug 20, 2015 at 11:14

3 votes

1 answer

388 views

Evaluating the limit of a quotient [Baby Rudin: 5.19]

asked Jun 11, 2015 at 20:45

3 votes

1 answer

182 views

Showing that the sum of these two closed subsets is a countable dense subset.

asked May 15, 2015 at 7:19

3 votes

0 answers

57 views

Intermediate "prime" extensions [Rotman]

asked Jun 28, 2015 at 3:47

2 votes

1 answer

444 views

Problems with P. Hall theorem proof (The problem involves the use of Frattini's argument)

asked Aug 21, 2015 at 10:36

2 votes

2 answers

242 views

Rudin 5.23(convergence of recursive sequence)

asked Aug 9, 2015 at 23:36

2 votes

2 answers

171 views

A finite group $G\neq \{1\}$ whose only characteristic subgroups are $\{1\}$ and $G$ is either simple or a direct product of isomorphic simple groups.

asked Aug 15, 2015 at 21:50

2 votes

1 answer

111 views

Isn't every set a G set?

asked Oct 24, 2015 at 3:59

2 votes

1 answer

288 views

Double cosets [Langs Algebra]

asked Oct 25, 2015 at 21:18

2 votes

2 answers

54 views

If $\varphi : G_1\to G_2$ is a group homorphism, can $\varphi(X)\leq G_2$ while $X\nleq G_1$.

asked Sep 18, 2015 at 23:31

Stack Exchange Network

81 Questions

Is every open set the interior of a closed set?

Why are subsets of compact sets not compact?

Proving $\lim\limits_{n\to \infty}\int\limits_{0}^{1} f_n(x)dx=0$

Showing a polynomial is irreducible in $\mathbb{Q}[x]$

Is $f(x)=\mu(V+x)$ continuous?

$x^p-a$ irreducible?

If $G$ is a $p$-group then $\Phi(G)=G'G^p$

Composition of a continuous function and a discontinuous function, can be continous.

Importance of compactness in Rudin problem.

Let $H,K\lhd G$, if $H\cong K$ and $H\cap K\neq\{1\}$ then does it follow that $H=K?$

If $K\lhd G$ and $(|K|,[G:K])=1$ then $K$ is characteristic.

Find all functions $\Phi$ on $[0,\infty)$ where $\Phi(\lim\limits_{p\to 0}||f||_p)=\int\limits_{0}^{1}(\Phi \circ f)d\mu$.

How would you go about writing $1/3=\sum\limits_{n=-k}^{\infty}a_n 2^{n}$ where $a_n=0,1$

Anyone Understand how the chain rule was applied here?

When does $L^r(\mu)=L^s(\mu)$?

Linearity of Uniformly Continuous functions

Understanding $\log p/q = \sum_{k=1}^{\infty} \frac{1}{2k-1}(\frac{p-q}{p+q})^{2k-1}$

Generating a countable mutually disjoint collection of arbitarally small measurable sets.

All analytic functions are constant?

Is $0\in (\bigcap\limits_{n=3}^{\infty}([0,1]-[1/n,1-1/n]))$

If a group $ G$ is not simple does it follow that it is isomorphic to the direct product of two nontrivial groups?

Evaluating the limit of a quotient [Baby Rudin: 5.19]

Showing that the sum of these two closed subsets is a countable dense subset.

Intermediate "prime" extensions [Rotman]

Problems with P. Hall theorem proof (The problem involves the use of Frattini's argument)

Rudin 5.23(convergence of recursive sequence)

A finite group $G\neq \{1\}$ whose only characteristic subgroups are $\{1\}$ and $G$ is either simple or a direct product of isomorphic simple groups.

Isn't every set a G set?

Double cosets [Langs Algebra]

If $\varphi : G_1\to G_2$ is a group homorphism, can $\varphi(X)\leq G_2$ while $X\nleq G_1$.