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Examples-counterexamples
New post in Examples-counterexamples
Counterexample: Convergence in finite dimensional distributions does not imply weak convergence
August 13th, 2020
examples-counterexamples
convergence-divergence
probability-distributions
weak-convergence
Application of Baire category theorem in Moore plane
August 10th, 2020
examples-counterexamples
baire-category
general-topology
The preimage of a Lebesgue measurable set under a measurable function need not be measurable
November 12th, 2020
measure-theory
real-analysis
examples-counterexamples
Operator with invertible adjoint
November 12th, 2020
functional-analysis
examples-counterexamples
Examples of Computations of the Divisor Class Group or Picard Group
August 1st, 2022
reference-request
algebraic-geometry
examples-counterexamples
Closed, orientable surface whose genus is very hard to find intuitively
August 1st, 2022
manifolds
examples-counterexamples
surfaces
education
general-topology
True/False Questions for Complex Analysis
August 1st, 2022
analyticity
complex-analysis
examples-counterexamples
Explicit example of a non-trivial zero of Riemann zeta function
August 1st, 2022
complex-analysis
riemann-zeta
examples-counterexamples
Topological counterexample: compact, Hausdorff, separable space which is not first-countable
August 1st, 2022
general-topology
compactness
first-countable
separable-spaces
examples-counterexamples
Examples of differentiable functions that are not of bounded variation
August 1st, 2022
bounded-variation
examples-counterexamples
real-analysis
When the sum of independent Markov chains is a Markov chain?
August 1st, 2022
examples-counterexamples
markov-chains
probability
probability-theory
Are primitive row stochastic matrices diagonalizable?
August 1st, 2022
linear-algebra
markov-chains
examples-counterexamples
matrices
Modules over Group algebra / representations example
August 1st, 2022
representation-theory
examples-counterexamples
modules
group-theory
abstract-algebra
Prove or disprove that the interior and the boundary of a connected set are connected.
August 1st, 2022
examples-counterexamples
general-topology
connectedness
continuous invertible map discontinuous inverse
August 1st, 2022
examples-counterexamples
general-topology
Example of a smooth 'step'-function that is constant below 0 and constant above 1
August 1st, 2022
analyticity
real-analysis
functions
examples-counterexamples
distribution-theory
Subspaces of $\ell^{2}$ and $\ell^{\infty}$ which are not closed?
August 1st, 2022
general-topology
functional-analysis
examples-counterexamples
lp-spaces
Example flat module but neither projective nor injective
August 1st, 2022
homological-algebra
examples-counterexamples
$A$ square matrix,nonsingular $\implies $ all submatrixes of $A$ are also nonsingular?
April 16th, 2020
examples-counterexamples
linear-algebra
matrices
Does the Laplace transform biject?
July 5th, 2020
functions
examples-counterexamples
laplace-transform
Sigma-algebra requirement 3, closed under countable unions.
August 1st, 2022
real-analysis
examples-counterexamples
measure-theory
Proving $f(C) \setminus f(D) \subseteq f(C \setminus D)$ and disproving equality
August 1st, 2022
functions
examples-counterexamples
elementary-set-theory
If $f$ is continuous on $[a,b)$ and $[b,c]$, then $f$ is Riemann integrable on $[a,c]$.
August 1st, 2022
partitions-for-integration
examples-counterexamples
real-analysis
riemann-sum
Example of application of the Uniform Boundedness Principle
August 1st, 2022
examples-counterexamples
functional-analysis
Examples of matrices that are both skew-symmetric and orthogonal
August 1st, 2022
matrices
examples-counterexamples
orthogonal-matrices
Examples of perfect sets.
August 1st, 2022
examples-counterexamples
measure-theory
analysis
Partition of the plane into union of open segments
August 1st, 2022
general-topology
examples-counterexamples
geometry
Applications of quadratic forms
August 6th, 2020
quadratic-forms
examples-counterexamples
big-list
Is the minimum of a parametric convex function convex again?
August 25th, 2020
convex-optimization
examples-counterexamples
convex-analysis
Rank of free submodules of a free module over a commutative ring.
August 1st, 2022
commutative-algebra
abstract-algebra
examples-counterexamples
modules
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