User Alexey

16 votes

1 answer

408 views

Can compacts on a real line behave "paradoxically" with respect to unions, intersections, and translation? What about other topological groups?

compactness topological-groups

asked Jul 20, 2013 at 19:45

13 votes

4 answers

2k views

Topological characterization of the closed interval $[0, 1]$.

general-topology

asked Mar 6, 2013 at 10:01

9 votes

4 answers

237 views

"Natural" proof of $P\left(\frac{d}{dx}\right)\bigl(e^{xy}Q(x)\bigr)=Q\left(\frac{d}{dy}\right)\bigl(e^{xy}P(y)\bigr)$.

ordinary-differential-equations polynomials exponential-function alternative-proof differential-operators

asked Dec 3, 2018 at 7:53

8 votes

1 answer

260 views

Intuition behind the injectivity part of Hurewicz Theorem

algebraic-topology soft-question homology-cohomology homotopy-theory cw-complexes

asked May 4, 2019 at 22:52

6 votes

1 answer

182 views

In what kind of rings a divisor of a product is a product of divisors?

ring-theory commutative-algebra soft-question terminology divisibility

asked Dec 30, 2018 at 17:50

5 votes

0 answers

200 views

Category theoretic definition of a "rank" of a subset of an algebraic structure

abstract-algebra category-theory

asked Feb 20, 2014 at 14:16

4 votes

2 answers

418 views

An example of a monomorphism that is not an equalizer in "Abstract and Concrete Categories -- The Joy of Cats"

category-theory abstract-algebra

asked Jul 20, 2013 at 19:16

4 votes

2 answers

644 views

"Canonical" symmetrization/skew-symmetrization/alternation of multilinear functions

soft-question tensor-products multilinear-algebra exterior-algebra universal-property

asked Jun 6, 2014 at 13:44

4 votes

0 answers

4k views

What are sliding vectors mathematically?

classical-mechanics affine-geometry

asked Oct 18, 2014 at 16:14

4 votes

1 answer

202 views

"Pivot step" that Donald Knuth mentioned in TAOCP

matrices numerical-linear-algebra gaussian-elimination sparse-matrices

asked Nov 18, 2017 at 16:05

3 votes

0 answers

228 views

Monads in monoids

abstract-algebra soft-question terminology monoid monads

asked Jun 19, 2016 at 8:21

3 votes

0 answers

52 views

Apparent (minor) error in Cauchy's article on pressure or tension in a solid body

analysis math-history tensors surface-integrals

asked Nov 22, 2016 at 10:22

3 votes

1 answer

176 views

Simplicial complexes of linear independencies

linear-algebra abstract-algebra soft-question terminology simplicial-complex

asked Jan 25, 2017 at 11:52

3 votes

1 answer

156 views

"Adjugate" of an endomorphism of a finite-rank free module

commutative-algebra modules exterior-algebra

asked Sep 28, 2014 at 11:37

3 votes

1 answer

870 views

If two points in a space are connected by a path, is there an injective map of an interval?

general-topology

asked Mar 6, 2013 at 8:16

3 votes

2 answers

544 views

Gödel's incompleteness theorems: where to learn? Is there a straightforward relation between the two?

reference-request logic incompleteness

asked Apr 16, 2014 at 13:01

2 votes

2 answers

333 views

A problem with lambda calculus notation and semantics for function-valued functions

functions notation lambda-calculus

asked Mar 22, 2013 at 11:59

2 votes

1 answer

68 views

Some weaker axiom than "no nontrivial zero divisors."

abstract-algebra ring-theory terminology axioms semigroups

asked May 8, 2015 at 17:50

2 votes

1 answer

234 views

Is there a recommended symbol for "equal by abuse of notation"?

notation

asked Jun 11, 2014 at 9:28

2 votes

1 answer

461 views

Most general definition of a normal vector to an affine subspace of a Euclidian space

linear-algebra reference-request soft-question vectors definition

asked Sep 24, 2018 at 14:56

2 votes

1 answer

238 views

Textbooks that use notation with explicit argument variable in the upper bound $\int^x$ for "indefinite integrals."

calculus reference-request notation indefinite-integrals

asked Jul 20, 2019 at 20:14

2 votes

1 answer

887 views

Notation for juxtaposition operation on matrices

linear-algebra matrices soft-question notation binary-operations

asked Mar 20, 2017 at 11:31

2 votes

2 answers

53 views

Term for elements of a monoid in a corresponding monid ring

abstract-algebra ring-theory terminology semigroups monoid

asked Apr 8, 2018 at 11:31

2 votes

0 answers

36 views

How to call the scalar "curl" of a vector field in a plane?

reference-request notation vector-analysis differential-operators curl

asked Dec 9, 2021 at 15:25

2 votes

1 answer

52 views

A simple example of a $G$-principal bundle that cannot be lifted to an $F$-principal bundle along an epimorphism $F\to G$.

algebraic-topology examples-counterexamples fiber-bundles principal-bundles spin-geometry

asked Apr 17 at 10:26

1 vote

1 answer

36 views

Are coslice categories of preadditive categories preadditive?

category-theory additive-categories

asked Jul 3, 2020 at 13:38

1 vote

0 answers

26 views

Relationship between modulus (absolute value) and algebraic norm.

complex-numbers field-theory galois-theory extension-field absolute-value

asked Oct 19, 2020 at 20:21

1 vote

0 answers

11 views

Classification of analytic involutions

functions analytic-functions involutions

asked Feb 13, 2021 at 21:15

1 vote

0 answers

140 views

Goldbach-like and Collatz-like conjectures and theorems

arithmetic big-list conjectures natural-numbers

asked Oct 1, 2021 at 18:48

1 vote

0 answers

35 views

Notation for equivalence relations between pairs of numbers that have the same difference or the same quotient

notation soft-question arithmetic

asked Oct 10, 2021 at 8:49

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48 Questions

Can compacts on a real line behave "paradoxically" with respect to unions, intersections, and translation? What about other topological groups?

Topological characterization of the closed interval $[0, 1]$.

"Natural" proof of $P\left(\frac{d}{dx}\right)\bigl(e^{xy}Q(x)\bigr)=Q\left(\frac{d}{dy}\right)\bigl(e^{xy}P(y)\bigr)$.

Intuition behind the injectivity part of Hurewicz Theorem

In what kind of rings a divisor of a product is a product of divisors?

Category theoretic definition of a "rank" of a subset of an algebraic structure

An example of a monomorphism that is not an equalizer in "Abstract and Concrete Categories -- The Joy of Cats"

"Canonical" symmetrization/skew-symmetrization/alternation of multilinear functions

What are sliding vectors mathematically?

"Pivot step" that Donald Knuth mentioned in TAOCP

Monads in monoids

Apparent (minor) error in Cauchy's article on pressure or tension in a solid body

Simplicial complexes of linear independencies

"Adjugate" of an endomorphism of a finite-rank free module

If two points in a space are connected by a path, is there an injective map of an interval?

Gödel's incompleteness theorems: where to learn? Is there a straightforward relation between the two?

A problem with lambda calculus notation and semantics for function-valued functions

Some weaker axiom than "no nontrivial zero divisors."

Is there a recommended symbol for "equal by abuse of notation"?

Most general definition of a normal vector to an affine subspace of a Euclidian space

Textbooks that use notation with explicit argument variable in the upper bound $\int^x$ for "indefinite integrals."

Notation for juxtaposition operation on matrices

Term for elements of a monoid in a corresponding monid ring

How to call the scalar "curl" of a vector field in a plane?

A simple example of a $G$-principal bundle that cannot be lifted to an $F$-principal bundle along an epimorphism $F\to G$.

Are coslice categories of preadditive categories preadditive?

Relationship between modulus (absolute value) and algebraic norm.

Classification of analytic involutions

Goldbach-like and Collatz-like conjectures and theorems

Notation for equivalence relations between pairs of numbers that have the same difference or the same quotient