User SOUL

3 votes

Find all functions $f:\mathbb{N}^+\to\mathbb{N}^+$ such that $f\big(f(n)\big)+f(n)=2n$ for every $n\in\mathbb{N}^+$.

answered Sep 25, 2018 at 5:56

3 votes

Prove that the set $A := \left\{ (x,y) \in \Bbb R_{> 0}^2 \mid xy \geq 1 \right\}$ is convex

answered Sep 26, 2018 at 3:23

3 votes

Accepted

How do I define the attaching map from $S^1$ to $S^1 \vee S^1\ $?

answered May 9, 2021 at 11:04

3 votes

Accepted

Show that $V\otimes V\simeq L(V^,V^,\mathbb{R})$

answered Feb 19, 2021 at 3:04

2 votes

Accepted

Splitting field over the field of fractions $\mathbb{Z}_p(x)$

answered May 9, 2021 at 2:59

2 votes

Accepted

Given a linear transformation and basis, verify $ [T]_{\beta}^{\alpha}[v]_{\alpha} = T[(v)]_{\beta}$ . (More details in description)

answered May 9, 2021 at 14:42

2 votes

How do you prove $ \sum_{n=1}^{\infty}{a_n} = \sum_{n=1}^{\infty}{a_{2n}} + \sum_{n=1}^{\infty}{a_{2n-1}} $

answered Nov 26, 2020 at 12:31

2 votes

function $f:\mathbb{R}→\mathbb{R}$ is monotone increasing, prove that $\lim_{x→c−} f(x) = \sup\{f(x):x < c\}$

answered Sep 12, 2018 at 2:36

2 votes

Is the set $\{ (x,y) \in \mathbb{R}^2 : xy=1 \}$ open or closed in $\mathbb{R}^2$

answered Nov 30, 2018 at 17:14

2 votes

Help with $\int_{0}^{\infty}\frac{1}{\sqrt{x^{5}+1}}dx$

answered Apr 27, 2020 at 17:39

1 vote

Complete metric space on the interval $[0,\infty)$

answered Apr 30, 2020 at 13:31

1 vote

$S_1 = [ |a -b| : a \in A , b \in B]$ What is the infimum and supremum of this set?

answered Sep 16, 2018 at 12:36

1 vote

If $x>0$ real number and $n>1$ integer, then $(1+x)^n>\frac{1}{2}n(n-1)x^2$

answered Sep 17, 2018 at 3:19

1 vote

Accepted

Show that for $a \ne 1$, $a > 0$ the sequence $\{x_n\} = n(1-a^{1\over n})$ is increasing

answered Nov 10, 2018 at 14:01

1 vote

Accepted

Determine whether the mappings are topologically conjugate

answered May 14, 2021 at 8:09

1 vote

Proving a result concerning quotient spaces.

answered May 8, 2021 at 3:33

1 vote

Real projective space and the fundamental group

answered Sep 7, 2021 at 7:10

1 vote

Accepted

Equivalent condition for continuity at a point.

answered Jun 19, 2022 at 7:46

1 vote

Accepted

$X$ can be embedded inside mapping cylinder $M_f$ by the map $x\mapsto [(x,0)]$ where $f:X\to Y$ is continuous

answered May 27, 2021 at 21:09

1 vote

Accepted

Relationship between reflexive space and separable space

answered May 28, 2021 at 16:39

1 vote

Real projective plane as an identification space of the Möbius strip.

answered Jun 7, 2021 at 9:50

0 votes

Accepted

Homeomorphism between a subspace of the complex projective space and $\mathbb C^n.$

answered Jun 6, 2021 at 15:18

0 votes

Find $Aut(\mathbb{C}*)$

answered Jul 13, 2021 at 2:42

0 votes

Show that the limit $a^x/x \to \infty$ when $a>1$ and $x \to \infty$

answered Sep 28, 2018 at 2:45

0 votes

A difficulty in understanding the proof of "Every convergent sequence is bounded"

answered Sep 10, 2018 at 2:34

0 votes

Prove directly that $a_n = 2^n / n!$ converges

answered Sep 12, 2018 at 2:20

0 votes

What is the reduced suspension of $I=[0,1]$?

answered Nov 2, 2020 at 1:15

-1 votes

Question on geometric realization of the torus.

answered May 23, 2021 at 17:04

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28 Answers

Find all functions $f:\mathbb{N}^+\to\mathbb{N}^+$ such that $f\big(f(n)\big)+f(n)=2n$ for every $n\in\mathbb{N}^+$.

Prove that the set $A := \left\{ (x,y) \in \Bbb R_{> 0}^2 \mid xy \geq 1 \right\}$ is convex

How do I define the attaching map from $S^1$ to $S^1 \vee S^1\ $?

Show that $V\otimes V\simeq L(V^,V^,\mathbb{R})$

Splitting field over the field of fractions $\mathbb{Z}_p(x)$

Given a linear transformation and basis, verify $ [T]_{\beta}^{\alpha}[v]_{\alpha} = T[(v)]_{\beta}$ . (More details in description)

How do you prove $ \sum_{n=1}^{\infty}{a_n} = \sum_{n=1}^{\infty}{a_{2n}} + \sum_{n=1}^{\infty}{a_{2n-1}} $

function $f:\mathbb{R}→\mathbb{R}$ is monotone increasing, prove that $\lim_{x→c−} f(x) = \sup\{f(x):x < c\}$

Is the set $\{ (x,y) \in \mathbb{R}^2 : xy=1 \}$ open or closed in $\mathbb{R}^2$

Help with $\int_{0}^{\infty}\frac{1}{\sqrt{x^{5}+1}}dx$

Complete metric space on the interval $[0,\infty)$

$S_1 = [ |a -b| : a \in A , b \in B]$ What is the infimum and supremum of this set?

If $x>0$ real number and $n>1$ integer, then $(1+x)^n>\frac{1}{2}n(n-1)x^2$

Show that for $a \ne 1$, $a > 0$ the sequence $\{x_n\} = n(1-a^{1\over n})$ is increasing

Determine whether the mappings are topologically conjugate

Proving a result concerning quotient spaces.

Real projective space and the fundamental group

Equivalent condition for continuity at a point.

$X$ can be embedded inside mapping cylinder $M_f$ by the map $x\mapsto [(x,0)]$ where $f:X\to Y$ is continuous

Relationship between reflexive space and separable space

Real projective plane as an identification space of the Möbius strip.

Homeomorphism between a subspace of the complex projective space and $\mathbb C^n.$

Find $Aut(\mathbb{C}*)$

Show that the limit $a^x/x \to \infty$ when $a>1$ and $x \to \infty$

A difficulty in understanding the proof of "Every convergent sequence is bounded"

Prove directly that $a_n = 2^n / n!$ converges

What is the reduced suspension of $I=[0,1]$?

Question on geometric realization of the torus.