User J.C.VegaO

4 votes

2 answers

126 views

number of real roots of $p(x) +p'(x)$

calculus polynomials

asked Sep 13, 2019 at 15:58

3 votes

1 answer

65 views

Is $E=\{(x,y) \in \mathbb R^2 | y^2-xy-x^3=0\}$ compact?

asked Feb 6, 2020 at 21:32

3 votes

2 answers

712 views

What are the operations in quaternions as a division ring?

abstract-algebra field-theory quaternions

asked Jun 23, 2020 at 21:50

3 votes

1 answer

39 views

if $A^X$ is a field, A being a ring, what can be concluded about $A$: field/ unital ring/ division ring?

abstract-algebra ring-theory

asked Jun 24, 2020 at 14:59

3 votes

1 answer

118 views

Proving ${\mathbb{P}}^n$ is Hausdorff

general-topology differential-geometry quotient-spaces projective-space

asked Nov 28, 2021 at 0:12

3 votes

1 answer

46 views

Each chart of the canonical structure of a submanifold S is locally a submanifold chart

differential-geometry manifolds submanifold

asked Dec 15, 2021 at 9:11

3 votes

1 answer

94 views

Making sense of the proof : The set $\{s_n(x)=(2/\pi)^{1/2} \sin nx:n \in \mathbb{N} \}$ is an orthonormal basis in $L^2[0,\pi]$- Rynne- Youngson

real-analysis functional-analysis hilbert-spaces

asked Jan 24 at 22:40

2 votes

0 answers

60 views

Is it enough to find $g$ not in $C([a,b])$ such that $f_{n}\rightarrow g$ in $||\cdot||_{p}$to conclude $(C[a,b],\|\cdot\|_p)$is not complete?

real-analysis general-topology functional-analysis complete-spaces

asked Jan 19 at 12:00

2 votes

1 answer

29 views

What is a sufficient condition for the singular values of a square matrix to be the modulus of its eigenvalues?

linear-algebra eigenvalues-eigenvectors singular-values

asked Dec 21, 2021 at 10:43

2 votes

2 answers

50 views

How to use Cauchy-Schwarz inequality to show the scalar product $\langle\xi,\eta\rangle=\sum_{i=1}^{\infty}\omega_i\xi_i\bar\eta_i$ is well-defined

real-analysis linear-algebra functional-analysis hilbert-spaces

asked Feb 6 at 13:14

2 votes

0 answers

76 views

How do I deal with the integration limits of the integrals that show up when showing that$Kx(t)=\int_0^tK(t,\tau)x(\tau)d\tau, x\in X$ is compact?

real-analysis functional-analysis operator-theory compact-operators

asked Feb 14 at 18:31

2 votes

1 answer

38 views

How do I prove $F_*Z=(Z^i\circ F^{-1})\partial_i'$, where Z is a field, and $(F(U),x\circ F^{-1})$ a chart with coordinate fields $\partial_i'$?

differential-geometry manifolds tangent-spaces

asked May 18 at 19:10

2 votes

1 answer

272 views

Why is a topological manifold defined with a countable basis?

general-topology manifolds

asked Feb 15, 2020 at 11:09

2 votes

1 answer

41 views

example for $\varphi(H \cap K) \subset \varphi(H)\cap \varphi(K)$, $H, K< G$ and $\varphi \in Hom(G,G')$

abstract-algebra group-theory

asked Jun 19, 2020 at 12:11

2 votes

0 answers

41 views

Definition of homeomorphism is missing continuity of $f$ in metric spaces

general-topology

asked Jul 6, 2020 at 17:01

2 votes

3 answers

137 views

Clarifying why compactness in a topology, implies compactness in a coarser topology

general-topology

asked Jul 7, 2020 at 18:45

2 votes

1 answer

83 views

$I_n \sim I_m $ iff $ n=m $ by induction over n

elementary-set-theory induction

asked Jun 15, 2020 at 19:26

2 votes

1 answer

72 views

Prove $\left<H\cup K\right>=H\lor K$

abstract-algebra group-theory

asked Jun 16, 2020 at 19:06

2 votes

5 answers

198 views

Train stops at $n$ stations

algebra-precalculus summation contest-math recreational-mathematics

asked Sep 13, 2019 at 16:52

2 votes

1 answer

752 views

image of a dense set via a continuous surjective function is dense

general-topology continuity

asked Nov 26, 2019 at 23:56

2 votes

1 answer

92 views

How do I prove there is a homeomorphism between these two topological spaces?

general-topology quotient-spaces

asked Feb 5, 2020 at 0:02

2 votes

0 answers

96 views

what is this function called in english?

general-topology terminology equivalence-relations quotient-spaces

asked Feb 5, 2020 at 10:34

1 vote

1 answer

52 views

Prove $f(x,y) = |x-y|(x-y)$ is a function of class $C^1$

multivariable-calculus continuity

asked Feb 2, 2020 at 20:12

1 vote

2 answers

469 views

Equation of parabola in x-y plane

linear-algebra analytic-geometry

asked Sep 13, 2019 at 18:52

1 vote

1 answer

273 views

Relationship between moment of inertia of a solid with respect to a point and moments of inertia with respect to the axes

multivariable-calculus classical-mechanics

asked Dec 28, 2019 at 16:58

1 vote

2 answers

221 views

Does Lagrange Multipliers method provide a way to classify relative minimum and maximum points?

multivariable-calculus

asked Jan 3, 2020 at 16:31

1 vote

1 answer

39 views

IS $(\mathbb{Z}_4,+) \rightarrow (\mathbb{Z}_5^{*},\cdot), n\pmod 4 \mapsto 2^n \pmod 5 $ well-defined??

abstract-algebra group-theory modular-arithmetic

asked Jun 17, 2020 at 22:55

1 vote

0 answers

74 views

Prove that $\mathbb{Z}_m$ and $\mathbb{Z}_n$ have the same cardinality iff m=n

abstract-algebra elementary-set-theory modular-arithmetic induction natural-numbers

asked Apr 2, 2020 at 21:24

1 vote

1 answer

68 views

How do I prove this topological space is T2 and compact?

general-topology compactness separable-spaces

asked Feb 3, 2020 at 23:54

1 vote

1 answer

50 views

What is wrong with my solution about the completeness of this metric space?

sequences-and-series metric-spaces solution-verification cauchy-sequences complete-spaces

asked Feb 6, 2020 at 11:13

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129 Questions

number of real roots of $p(x) +p'(x)$

Is $E=\{(x,y) \in \mathbb R^2 | y^2-xy-x^3=0\}$ compact?

What are the operations in quaternions as a division ring?

if $A^X$ is a field, A being a ring, what can be concluded about $A$: field/ unital ring/ division ring?

Proving ${\mathbb{P}}^n$ is Hausdorff

Each chart of the canonical structure of a submanifold S is locally a submanifold chart

Making sense of the proof : The set $\{s_n(x)=(2/\pi)^{1/2} \sin nx:n \in \mathbb{N} \}$ is an orthonormal basis in $L^2[0,\pi]$- Rynne- Youngson

Is it enough to find $g$ not in $C([a,b])$ such that $f_{n}\rightarrow g$ in $||\cdot||_{p}$to conclude $(C[a,b],\|\cdot\|_p)$is not complete?

What is a sufficient condition for the singular values of a square matrix to be the modulus of its eigenvalues?

How to use Cauchy-Schwarz inequality to show the scalar product $\langle\xi,\eta\rangle=\sum_{i=1}^{\infty}\omega_i\xi_i\bar\eta_i$ is well-defined

How do I deal with the integration limits of the integrals that show up when showing that$Kx(t)=\int_0^tK(t,\tau)x(\tau)d\tau, x\in X$ is compact?

How do I prove $F_*Z=(Z^i\circ F^{-1})\partial_i'$, where Z is a field, and $(F(U),x\circ F^{-1})$ a chart with coordinate fields $\partial_i'$?

Why is a topological manifold defined with a countable basis?

example for $\varphi(H \cap K) \subset \varphi(H)\cap \varphi(K)$, $H, K< G$ and $\varphi \in Hom(G,G')$

Definition of homeomorphism is missing continuity of $f$ in metric spaces

Clarifying why compactness in a topology, implies compactness in a coarser topology

$I_n \sim I_m $ iff $ n=m $ by induction over n

Prove $\left<H\cup K\right>=H\lor K$

Train stops at $n$ stations

image of a dense set via a continuous surjective function is dense

How do I prove there is a homeomorphism between these two topological spaces?

what is this function called in english?

Prove $f(x,y) = |x-y|(x-y)$ is a function of class $C^1$

Equation of parabola in x-y plane

Relationship between moment of inertia of a solid with respect to a point and moments of inertia with respect to the axes

Does Lagrange Multipliers method provide a way to classify relative minimum and maximum points?

IS $(\mathbb{Z}_4,+) \rightarrow (\mathbb{Z}_5^{*},\cdot), n\pmod 4 \mapsto 2^n \pmod 5 $ well-defined??

Prove that $\mathbb{Z}_m$ and $\mathbb{Z}_n$ have the same cardinality iff m=n

How do I prove this topological space is T2 and compact?

What is wrong with my solution about the completeness of this metric space?