Notable Question - Badge - Mathematics Stack Exchange

Notable Question

Question with 2,500 views. This badge can be awarded multiple times.

Diane Vanderwaif

4,2647 gold badges43 silver badges103 bronze badges

earned this badge 31 times.

Let $X=\{1,2,3\}$. Find all topology of $X$ which are either $T_0$, or $T_1$, or $T_3$

Awarded Jun 13 at 4:56

Prove that a subset $A$ of $X$ is dense if and only if every open subset of $ X$ contain some point of $A$

Awarded Feb 15 at 9:03

A certain tree $T$ of order $n$ contains only vertices of degree $1$ and $3$. Show that $T$ contain $\frac{n-2}{2}$ vertices of degree $3$.

Awarded Jan 24 at 9:18

Prove that if $f^2=g^2$ and $f(x)$ not zero then $f(x)=g(x)$ or $f(x)=-g(x)$

Awarded Nov 3, 2022 at 14:56

Prove that if $deg(u)+deg(v)\geq n$ for every pair $u.v$ of non adjacent vertices of $G$, then $G$ is non-separable.

Awarded Jun 17, 2022 at 8:04

Write the complex number $1 + \cos \alpha +i \sin \alpha$ in polar form

Awarded Jun 6, 2022 at 13:05

Prove for any given positive integer $N$ there exist only finitely many integers n with $φ(n)=N$ [duplicate]

Awarded Apr 28, 2022 at 9:35

Internal and external direct products of finite groups are isomorphic.

Awarded Dec 13, 2021 at 14:08

Prove or disprove: $|\sin z|<1$ for all $z \in \mathbb C$

Awarded Apr 6, 2021 at 12:32

Suppose that $f$ is analytic on a close curve γ. Prove or disprove $\int_\gamma \overline{f(z)}f'(z)dz$ is purely imaginary.

Awarded Dec 4, 2020 at 18:27

Prove that if a function $f$ has a jump at an interior point of the interval $[a,b]$ then it cannot be the derivative of any function.

Awarded Dec 1, 2020 at 0:16

Prove or disprove that if $f$ is continuous function and $A$ is closed, then $\,f[A]$ is closed.

Awarded Oct 7, 2020 at 1:57

Prove that $X$ is compact if and only if every cover of $X$ by members of $B$ has finite subcover.

Awarded Jun 26, 2020 at 11:50

Prove that if $\delta(G) \geq 2$ then $G$ contain a cycle

Awarded Apr 29, 2020 at 19:03

Prove that every $k$-chromatic graph has size $m\geq \binom k2 $

Awarded Mar 27, 2020 at 19:05

The limit as $x \to \infty$ of $ \frac {\sqrt{x+ \sqrt{ x+\sqrt x}} }{\sqrt{x+1}}$

Awarded Mar 24, 2020 at 11:15

Prove that if $G$ has a Hamiltonian path then $k(G-S)≤|S|+1$ for every non-empty proper subset $S$ of $V(G)

Awarded Feb 2, 2020 at 12:15

Prove that $f$ is not integrable on $[0,1]$

Awarded Oct 27, 2019 at 18:55

Prove that if $deg(u)+deg(v) \geq n-1$ for every two non adjacent vertices $u$ and $v$ of $G$ then $G$ is connected and $diam(G) \leq 2$

Awarded Jan 20, 2019 at 15:05

Prove that the set of one-to-one function $f: S\to S$ is a group with composition as group operation.

Awarded Jan 18, 2019 at 7:00

If a function $f$ is continuous in $[a,∞)$ and finite $\lim_{x→+∞}⁡f(x)$ exists, then it's uniformly continuous in $[a,+∞)$.

Awarded Nov 19, 2018 at 14:45

Prove that if $f:A\to B$ is uniformly continuous on $A$ and $g$ is uniformly continuous on $B$, then $g(f(x))$ is uniformly continuous on $A$

Awarded Oct 25, 2018 at 0:20

Subsequence of $\sin n$

Awarded Aug 6, 2018 at 21:30

Prove that a 3-regular graph $G$ has a cut-vertex if and only if $G$ has a bridge.

Awarded Aug 1, 2018 at 1:15

Prove that if $d$ divides $n$ then $φ(d)$ divide $φ(n)$ for $φ$ denotes Euler’s φ-function.

Awarded Feb 14, 2018 at 21:29

Smooth function proof

Awarded Nov 10, 2017 at 21:30

Limit of absolute value of sequence

Awarded Oct 17, 2017 at 19:57

Prove that every connected graph of all whose vertices have even degree contain no bridges.

Awarded Oct 13, 2016 at 8:12

bifurcation value

Awarded Feb 4, 2016 at 10:19

closed and open set - set $S$ is open if and only if its complement is closed?

Awarded Sep 24, 2015 at 7:59

Prove that the min and max of 2 continuous function are continuous

Awarded Aug 31, 2015 at 0:53

Others with this badge