User edm

9 votes

2 answers

2k views

How to use Stokes theorem in the presence of holes?

asked Oct 15, 2017 at 11:42

7 votes

2 answers

970 views

How rough can differential form, manifold and chain be for Stokes theorem to hold?

smooth-manifolds differential-forms stokes-theorem

asked Nov 16, 2017 at 3:04

7 votes

6 answers

2k views

If two topological spaces have the same topological properties, are they homeomorphic?

general-topology

asked Oct 30, 2016 at 1:09

6 votes

2 answers

383 views

Intrinsic, coordinate-free interpretation of "inverse" of a metric tensor

differential-geometry tensors

asked Mar 12, 2018 at 18:43

5 votes

1 answer

126 views

What makes a Riemannian manifold "directionally homogeneous"?

differential-geometry riemannian-geometry

asked Nov 28, 2017 at 7:53

5 votes

2 answers

674 views

Why don't we consider "Hamiltonian vector field" on tangent bundle?

soft-question riemannian-geometry classical-mechanics symplectic-geometry tangent-bundle

asked Dec 11, 2017 at 15:45

5 votes

2 answers

910 views

Is it "identity function is diffeomorphism" implies the two smooth structures are equal?

proof-verification differential-topology smooth-manifolds

asked Aug 8, 2017 at 3:01

5 votes

3 answers

369 views

Axiom of dependent choice and a problem about metric spaces

metric-spaces axiom-of-choice

asked Sep 26, 2016 at 10:38

5 votes

1 answer

764 views

Do scalar integrals correspond to integration of differential forms?

multivariable-calculus differential-geometry differential-topology smooth-manifolds differential-forms

asked Jun 14, 2017 at 8:38

4 votes

2 answers

433 views

Area swept by a moving line

geometry

asked Mar 22, 2017 at 16:39

4 votes

2 answers

454 views

Possible error in a proof in Jost's Riemannian Geometry and Geometric Analysis

functional-analysis differential-geometry riemannian-geometry

asked Dec 21, 2017 at 4:29

4 votes

2 answers

579 views

How to define a topological space of straight lines?

general-topology reference-request smooth-manifolds grassmannian

asked Sep 5, 2017 at 8:39

4 votes

1 answer

448 views

While Fourier series solve heat equation on a finite interval, can Fourier transform solve heat equation on infinite line?

partial-differential-equations fourier-analysis heat-equation

asked Jul 4, 2019 at 18:09

3 votes

1 answer

211 views

What makes a metric space have the property "bounded set is totally bounded"?

general-topology metric-spaces

asked Apr 27, 2017 at 2:31

3 votes

0 answers

41 views

How should I interpret "two discs intersect along an arc" and "union of discs" from Armstrong's Basic Topology?

general-topology

asked Feb 11, 2017 at 13:40

3 votes

2 answers

719 views

Multiplicative group modulo n isomorphism

abstract-algebra elementary-number-theory ring-theory

asked Mar 10, 2017 at 2:54

3 votes

1 answer

173 views

Two manifolds $X$ and $Y$ with two bijective continuous functions from $X$ to $Y$ and $Y$ to $X$, but not homeomorphic

general-topology

asked Dec 10, 2016 at 13:21

3 votes

2 answers

490 views

Does the definition of distribution and Dirac delta function capture the physicists' idea?

distribution-theory dirac-delta

asked Aug 21, 2016 at 13:58

2 votes

3 answers

835 views

Different versions of Bolzano-Weierstrass theorem

real-analysis analysis

asked Sep 22, 2016 at 11:36

2 votes

1 answer

99 views

How do we know that topological spaces and groups are essentially different?

category-theory

asked Jan 6, 2017 at 9:59

2 votes

5 answers

211 views

Equality of dimension of $\bigwedge^2(\Bbb R^n)$ and $\text{SO}(n)$

manifolds lie-groups exterior-algebra

asked Oct 12, 2016 at 14:19

2 votes

0 answers

51 views

Can we always find spin operators?

linear-algebra matrices representation-theory quantum-mechanics

asked Oct 26, 2019 at 13:50

2 votes

1 answer

100 views

When is the matrix $I-P$ nilpotent?

matrices discrete-mathematics modular-arithmetic recreational-mathematics nilpotence

asked Apr 4, 2019 at 7:52

2 votes

0 answers

215 views

What are the higher-dimensional generalisation of intermediate value theorem and bisection method?

reference-request algebraic-topology

asked Mar 26, 2018 at 4:35

2 votes

1 answer

316 views

How should we prove equivalence of definitions?

logic proof-writing proof-theory

asked Jan 30, 2017 at 16:54

2 votes

1 answer

443 views

How do I know that these definitions of inner product of $k$-vectors and Hodge star are well-defined?

linear-algebra riemannian-geometry inner-products tensors multilinear-algebra

asked Aug 31, 2017 at 9:39

1 vote

0 answers

103 views

Derivation of Euler-Lagrange equation: locally stationary in what sense?

calculus-of-variations euler-lagrange-equation

asked Aug 11, 2017 at 12:13

1 vote

1 answer

478 views

Books and references for Möbius transformation, hyperbolic Riemann surface and covering transformation

reference-request book-recommendation riemann-surfaces mobius-transformation

asked Feb 28, 2018 at 17:33

1 vote

0 answers

81 views

What does $\lim\limits_{h\to0}\frac{\lVert f(x+h)-f(x)-L(h)+\cdots\rVert}{\lVert h\rVert^k}=0$, $k\gt1$, tell us about the function $f$?

multivariable-calculus derivatives

asked Oct 4, 2018 at 16:14

1 vote

1 answer

120 views

Does existence of nonzero linear functional depends on axiom of choice? [duplicate]

vector-spaces axiom-of-choice

asked Jul 9, 2017 at 12:07

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37 Questions

How to use Stokes theorem in the presence of holes?

How rough can differential form, manifold and chain be for Stokes theorem to hold?

If two topological spaces have the same topological properties, are they homeomorphic?

Intrinsic, coordinate-free interpretation of "inverse" of a metric tensor

What makes a Riemannian manifold "directionally homogeneous"?

Why don't we consider "Hamiltonian vector field" on tangent bundle?

Is it "identity function is diffeomorphism" implies the two smooth structures are equal?

Axiom of dependent choice and a problem about metric spaces

Do scalar integrals correspond to integration of differential forms?

Area swept by a moving line

Possible error in a proof in Jost's Riemannian Geometry and Geometric Analysis

How to define a topological space of straight lines?

While Fourier series solve heat equation on a finite interval, can Fourier transform solve heat equation on infinite line?

What makes a metric space have the property "bounded set is totally bounded"?

How should I interpret "two discs intersect along an arc" and "union of discs" from Armstrong's Basic Topology?

Multiplicative group modulo n isomorphism

Two manifolds $X$ and $Y$ with two bijective continuous functions from $X$ to $Y$ and $Y$ to $X$, but not homeomorphic

Does the definition of distribution and Dirac delta function capture the physicists' idea?

Different versions of Bolzano-Weierstrass theorem

How do we know that topological spaces and groups are essentially different?

Equality of dimension of $\bigwedge^2(\Bbb R^n)$ and $\text{SO}(n)$

Can we always find spin operators?

When is the matrix $I-P$ nilpotent?

What are the higher-dimensional generalisation of intermediate value theorem and bisection method?

How should we prove equivalence of definitions?

How do I know that these definitions of inner product of $k$-vectors and Hodge star are well-defined?

Derivation of Euler-Lagrange equation: locally stationary in what sense?

Books and references for Möbius transformation, hyperbolic Riemann surface and covering transformation

What does $\lim\limits_{h\to0}\frac{\lVert f(x+h)-f(x)-L(h)+\cdots\rVert}{\lVert h\rVert^k}=0$, $k\gt1$, tell us about the function $f$?

Does existence of nonzero linear functional depends on axiom of choice? [duplicate]