User Madrit Zhaku

3 votes

3 answers

169 views

Prove the equation $\vert d(x,z)-d(y,t)\vert\leq d(x,y)+d(z,t)$

asked Jul 30, 2014 at 15:09

0 votes

1 answer

144 views

If there is the inverse operator of the operator A, then $(A^{-1})^{-1}=A$?

asked Jul 27, 2014 at 16:44

-2 votes

1 answer

148 views

Are there infinite metric spaces which have no infinite compact subsets

asked Jan 5, 2014 at 19:08

0 votes

1 answer

25 views

Find an example of metric space which is not true the follow equation $\overline {T(x_0,r)}\subset T[x,r]=\{x:d(x,x_0 \leq r)\}$

asked Jan 4, 2014 at 20:23

0 votes

2 answers

736 views

Show that finite set no accumulation points

asked Jan 3, 2014 at 18:07

0 votes

1 answer

908 views

Diameters of and distances between sets in metric spaces

asked Nov 15, 2013 at 18:47

1 vote

2 answers

121 views

Tell that sequence $(x_n)$ converges if and only if there $n_0\in \Bbb N$ such that $x_n=x_{n_0}$ for all $n\geq n_0.$*

asked Nov 12, 2013 at 18:48

1 vote

2 answers

594 views

Two equivalent definitions of convergent sequences?

asked Nov 9, 2013 at 20:19

0 votes

2 answers

215 views

How to prove that $(\mathbb{Z}, d)$ with $d(m,n)=\vert m -n \vert$ is complete

asked Nov 8, 2013 at 16:34

0 votes

2 answers

182 views

If $\{x\}$ is an open set in $X$, for all $x\in X$, then all subsets of $X$ is open in $X$

asked Nov 8, 2013 at 10:42

0 votes

1 answer

197 views

The set $F_1\subset X_1$ is closed set in $X_1$ if and only if there is an closed set $F$ in $X$ such that $F\cap X_1=F_1$

asked Nov 7, 2013 at 18:46

1 vote

2 answers

2k views

Finding the closure of $\mathbb{Z}$ and $\mathbb{Q}$ in $\mathbb{R}$

asked Nov 6, 2013 at 12:56

3 votes

3 answers

3k views

Show that interval $(a, b)$ is not open in $\mathbb{R}^2$

asked Nov 3, 2013 at 16:49

0 votes

2 answers

260 views

How to prove properties of the family of closed sets in a metric space

asked Nov 3, 2013 at 10:39

0 votes

3 answers

44 views

How to tell $\overline {(a,b)}=[a,b]$, $\overline{\{\frac{1}{n}:n=1,2,3,\ldots}\}=\{\frac{1}{n}:n=1,2,3,\ldots\}\cup \{0\}$

asked Nov 2, 2013 at 18:35

1 vote

1 answer

81 views

Whether a function$d(m,n)=\left\vert\frac{1}{m}-\frac{1}{n}\right\vert$ metrics

asked Oct 29, 2013 at 18:46

1 vote

1 answer

198 views

Prove that the vector space $\Phi ^ T$ is algebra on $\Phi$

asked Oct 26, 2013 at 20:12

3 votes

1 answer

933 views

Please help me prove: $v(a+b)\leq v(a)+v(b)$, and $v(ab)\leq v(a)v(b)$ where $v(x)=\inf{\{\vert x^n \vert}^{1/n}: n\in\mathbb{N}\}$

asked Oct 23, 2013 at 17:27

0 votes

1 answer

84 views

Help me please proving the theorem

asked Oct 11, 2013 at 12:19

1 vote

3 answers

318 views

Prove this inequality: $|a_1b_1+a_2b_2+\cdots+ a_nb_n|\leq 1$ for two normalised vectors

asked Jul 15, 2012 at 14:56

1 vote

2 answers

91 views

How to prove that $a^2(1+b^2)+b^2(1+c^2)+c^2(1+a^2)\geq6abc$

asked Jul 15, 2012 at 14:44

6 votes

4 answers

10k views

How to evaluate $\int 1/(1+x^{2n})\,dx$ for an arbitrary positive integer $n$? [duplicate]

asked Jul 15, 2012 at 7:46

0 votes

3 answers

222 views

Please help me for a substitution method to evaluate $\int\frac{dx}{(x+a)^2(x+b)^2}$ [closed]

asked Jul 7, 2012 at 18:59

-1 votes

3 answers

358 views

If $|f| \leq A + B|z|^k$ then $f$ is polynomial

asked Jul 2, 2012 at 19:33

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24 Questions

Prove the equation $\vert d(x,z)-d(y,t)\vert\leq d(x,y)+d(z,t)$

If there is the inverse operator of the operator A, then $(A^{-1})^{-1}=A$?

Are there infinite metric spaces which have no infinite compact subsets

Find an example of metric space which is not true the follow equation $\overline {T(x_0,r)}\subset T[x,r]=\{x:d(x,x_0 \leq r)\}$

Show that finite set no accumulation points

Diameters of and distances between sets in metric spaces

Tell that sequence $(x_n)$ converges if and only if there $n_0\in \Bbb N$ such that $x_n=x_{n_0}$ for all $n\geq n_0.$*

Two equivalent definitions of convergent sequences?

How to prove that $(\mathbb{Z}, d)$ with $d(m,n)=\vert m -n \vert$ is complete

If $\{x\}$ is an open set in $X$, for all $x\in X$, then all subsets of $X$ is open in $X$

The set $F_1\subset X_1$ is closed set in $X_1$ if and only if there is an closed set $F$ in $X$ such that $F\cap X_1=F_1$

Finding the closure of $\mathbb{Z}$ and $\mathbb{Q}$ in $\mathbb{R}$

Show that interval $(a, b)$ is not open in $\mathbb{R}^2$

How to prove properties of the family of closed sets in a metric space

How to tell $\overline {(a,b)}=[a,b]$, $\overline{\{\frac{1}{n}:n=1,2,3,\ldots}\}=\{\frac{1}{n}:n=1,2,3,\ldots\}\cup \{0\}$

Whether a function$d(m,n)=\left\vert\frac{1}{m}-\frac{1}{n}\right\vert$ metrics

Prove that the vector space $\Phi ^ T$ is algebra on $\Phi$

Please help me prove: $v(a+b)\leq v(a)+v(b)$, and $v(ab)\leq v(a)v(b)$ where $v(x)=\inf{\{\vert x^n \vert}^{1/n}: n\in\mathbb{N}\}$

Help me please proving the theorem

Prove this inequality: $|a_1b_1+a_2b_2+\cdots+ a_nb_n|\leq 1$ for two normalised vectors

How to prove that $a^2(1+b^2)+b^2(1+c^2)+c^2(1+a^2)\geq6abc$

How to evaluate $\int 1/(1+x^{2n})\,dx$ for an arbitrary positive integer $n$? [duplicate]

Please help me for a substitution method to evaluate $\int\frac{dx}{(x+a)^2(x+b)^2}$ [closed]

If $|f| \leq A + B|z|^k$ then $f$ is polynomial