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Diane Vanderwaif

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earned this badge 87 times.

Prove that subset $F$ of a metric space $X,D$ is closed if and only if $X-F$ is open

Awarded 2 days ago

Proof that $\limsup (a_nb_n)=\limsup a_n \lim b_n$

Awarded Oct 13 at 13:58

Is $\operatorname{SL}_n(\mathbb{R})$ a normal subgroup in $\operatorname{GL}_n(\mathbb{R})$?

Awarded Aug 3 at 19:41

Does this graph contain $K_5$ or $K_{3,3}$ as subdivision or minor?

Awarded Jul 6 at 18:08

prove that if $L(f,P)=U(f,P)$ then $f$ is constant on $[a,b]$

Awarded Jun 3 at 12:36

Increasing and bounded sequence proof

Awarded Jan 5 at 4:36

Uniform continuous function proof

Awarded Oct 20, 2022 at 16:51

Find an example of a regular triangle-free $4$-chromatic graph

Awarded Oct 11, 2022 at 21:16

prove that $\int(f(x)+g(x))dx= \int f(x)dx+\int g(x)dx$

Awarded Oct 4, 2022 at 3:46

Prove that there exist regular tournament of every odd order but there is no regular tournament of even order.

Awarded Sep 5, 2022 at 12:09

Matrices inversion proof: $A(I-A)^{-1}=(I-A)^{-1} A$

Awarded Jul 4, 2022 at 18:41

prove or disprove that $CL(A∩B)=CL(A)∩CL(B)$

Awarded Mar 30, 2022 at 21:17

Prove that every outer planar graph is $3$-choosable

Awarded Dec 2, 2021 at 16:15

Use following Theorem to show that every tree has at most one perfect matching.

Awarded Nov 30, 2021 at 20:36

Find a necessary and sufficient condition for the Cartesian product $G \times H$ is Eulerian, for $G$ and $H$ are non trivial connected graphs.

Awarded Oct 29, 2021 at 6:40

Find a map of the solid torus into itself having no fixed point. Where does the proof of the Brouwer theorem fail.

Awarded Oct 28, 2021 at 23:35

Prove that if $G$ is $k$-edge connected, then $G \bigvee K_1$ is $k+1$-edge connected.

Awarded Oct 25, 2021 at 20:05

Prove that if a set $A \subset \mathbb R^n$ is connected, then it has the Intermediate Value Property.

Awarded Jul 12, 2021 at 4:37

Prove that if $deg (v) > \frac{k}{2}$ for every $v \in V(G)$ then $G$ is Hamitonian.

Awarded Jun 25, 2021 at 13:48

Logistic population model question

Awarded Jun 10, 2021 at 15:36

Describe the image of the set $\{z:|z|<1, Im(z)>0\}$ under the mapping $w =\frac{2z-i}{2+iz}$

Awarded May 26, 2021 at 11:06

Prove that$ H_x (X)$ does not depend on the choice of local parametrization.

Awarded May 13, 2021 at 22:09

If $σ^2$ is the identity map from $G$ to $G$, prove that $G$ is abelian.

Awarded Apr 12, 2021 at 23:11

Prove that no bipartite graph of order $3$ or more is Hamiltonian connected

Awarded Mar 26, 2021 at 5:17

Prove that if $Re(z^n)\geq 0$ for every positive $n$ then $z\in \mathbb C$ is nonnegative real number

Awarded Mar 10, 2021 at 2:05

Prove or disprove if $G$ is 2-edge-connected then there exist 2 edges disjoint $u-v$ trail such that every edge of $G$ lies on one of these trails.

Awarded Feb 27, 2021 at 11:36

Prove that every nontrivial tournament has at least one serf.

Awarded Feb 8, 2021 at 17:35

Find an example of a compact space which is not locally compact.

Awarded Jan 15, 2021 at 15:27

Determine a formula for the number of triangles in the line graph $L(G)$ in term of quantities in $G$

Awarded Dec 4, 2020 at 12:41

Describe the image of the set $\{z=x+iy:x>0,y>0\}$ under the mapping $w=\frac{z-i}{z+i}$

Awarded Dec 4, 2020 at 9:35

Prove directly that the space $\mathbb{R}$ of real number with usual absolute value metric is second countable.

Awarded Nov 11, 2020 at 8:50

Prove that $G$ is $k$ connected iff for each 2-vertex $T \subset S$, there is a cycle of $G$ that contain both vertices in $T$

Awarded Nov 4, 2020 at 8:36

Prove that if $S^k$ has a non vanishing vector field, then its antipodal map is homotopy to the identity if $k$ is even.

Awarded Nov 3, 2020 at 6:17

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

Awarded Oct 29, 2020 at 9:43

Prove that if $G$ is a $k$-connected graph, then $G \vee K_1$ is a $(k+1)$-connected graph

Awarded Oct 19, 2020 at 16:16

Let $a_n$ be a convergent sequence wit limit $L$. With out using the Heine-Borel theorem, prove that the set $\{L,a_1,a_2,...\}$ is compact.

Awarded Oct 4, 2020 at 1:02

Prove that any subset of any countable set $S$ is countable

Awarded Jul 14, 2020 at 9:58

Find an analytic function that maps the angle $-\pi/4<\operatorname{arg}(z)<\pi/2$ onto the upper half plane so that $w(1-i)=2,w(i)=-1$, and $w(0)=0$

Awarded Jun 8, 2020 at 4:26

Prove that every planar graph is $6$-choosable without using Thomassens's theorem

Awarded May 4, 2020 at 17:18

Prove that a graph $G$ is a forest if and only if every induced subgraph of $G$ contain a vertex of degree at most $1$

Awarded Apr 5, 2020 at 21:15

Does a continuous function commute with $\limsup$ of bounded sequences?

Awarded Feb 20, 2020 at 11:10

Determine the set of points $z$ that satisfy the condition $|2z|>|1+z^2|$

Awarded Feb 16, 2020 at 7:40

Prove that if $G$ is an $r$-regular, $(r-2)$-edge-connected graph of even order containing at most $r-1$ distinct edge cuts then $G$ has a $1$-factor

Awarded Feb 3, 2020 at 17:20

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 Feb 2, 2020 at 19:15

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

Awarded Dec 4, 2019 at 10:50

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

Awarded Oct 23, 2019 at 15:25

Show that Möbius transformation $S$ commute with $T$ if $S$ and $T$ have the same fixed point.

Awarded Oct 18, 2019 at 16:20

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

Awarded Oct 12, 2019 at 9:20

Describe how to obtain a sphere in $\mathbb R^3$ as a quotient of a closed disk in $\mathbb R^2$

Awarded Aug 28, 2019 at 9:50

a graph $G$ of order $n \geq 2k$ is $k$ connected iff there exist $k$ pairwise disjoint paths connecting $V_1$ and $V_2$

Awarded Apr 4, 2019 at 1:50

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 Mar 4, 2019 at 9:45

Proof for limit superior's property: $\limsup (a_n b_n ) \leq \limsup a_n \cdot \limsup b_n$ [duplicate]

Awarded Jan 1, 2019 at 9:25

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

Awarded Nov 21, 2018 at 15:20

Prove that if $G$ and $H$ is Hamiltonian then $G \times H$ is Hamiltonian

Awarded Oct 24, 2018 at 20:35

Prove that if sets $A$ and $B$ are closed and bounded then $A+B$ is closed

Awarded Sep 30, 2018 at 17:50

Find an analytic function that maps the plane with the slit $[-1,1]$ onto the upper half plane

Awarded Sep 9, 2018 at 18:10

Use the divergent theorem to verify the volume of a circular cone

Awarded Aug 17, 2018 at 0:15

Find probability in card question

Awarded Aug 3, 2018 at 15:50

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 Jul 24, 2018 at 18:15

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

Awarded May 19, 2018 at 18:48

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