Categories
Tags
Examples-counterexamples
New post in Examples-counterexamples
Function that is Riemann-Stieltjes integrable but not Riemann integrable?
August 1st, 2022
integration
stieltjes-integral
examples-counterexamples
riemannian-geometry
A complex function that is harmonic but not analytic
August 1st, 2022
harmonic-functions
analyticity
complex-analysis
examples-counterexamples
Is the sum of two singular matrices also singular?
August 1st, 2022
examples-counterexamples
linear-algebra
matrices
locally compact Hausdorff space which is not second-countable
August 1st, 2022
examples-counterexamples
compactness
second-countable
general-topology
an example of a continuous bijection which is not a homeomorphism
August 1st, 2022
examples-counterexamples
general-topology
Give an example of a nonabelian group in which a product of elements of finite order can have infinite order.
August 1st, 2022
examples-counterexamples
abstract-algebra
abelian-groups
group-theory
Sequence with all rationals as limit points
August 1st, 2022
real-analysis
examples-counterexamples
sequences-and-series
Example where closure of $A+B$ is different from sum of closures of $A$ and $B$
August 1st, 2022
examples-counterexamples
general-topology
sumset
If $\{x_n\}$ satisfies that $x_{n+1} - x_n$ goes to $0$, is $\{x_n\}$ a Cauchy sequence?
August 1st, 2022
sequences-and-series
examples-counterexamples
cauchy-sequences
A set that it is uncountable, has measure zero, and is not compact
August 1st, 2022
real-analysis
measure-theory
examples-counterexamples
Proof intersection is finite and non-empty
April 18th, 2020
examples-counterexamples
real-analysis
elementary-set-theory
Convergence Counterexamples
September 19th, 2021
examples-counterexamples
analysis
convergence-divergence
big-list
What is an example of a function that is measurable but not strongly measurable?
August 1st, 2022
examples-counterexamples
integration
measure-theory
functional-analysis
Examples of interesting and creative problems about differentiation (in one variable)
January 20th, 2020
derivatives
big-list
examples-counterexamples
calculus
Example of a function in $L^2(\mathbb{R})$ with derivative not in $L^2(\mathbb{R})$.
August 1st, 2022
examples-counterexamples
lebesgue-integral
derivatives
functional-analysis
Is there a regular not completely regular space which is not a corkscrew?
October 11th, 2020
general-topology
examples-counterexamples
Continuous bijections from the open unit disc to itself - existence of fixed points
January 29th, 2020
fixed-point-theorems
analysis
real-analysis
examples-counterexamples
Counterexample for the Open Mapping Theorem
June 4th, 2020
examples-counterexamples
functional-analysis
Nonmeasurable set with positive outer measure
August 1st, 2022
examples-counterexamples
measure-theory
A Hausdorff space which is not completely regular
August 1st, 2022
examples-counterexamples
general-topology
Counterexample to Rellich-Kondrachov Compactness Theorem, case $q=p^*$
August 1st, 2022
sobolev-spaces
lp-spaces
partial-differential-equations
examples-counterexamples
Example of Converge in measure, but not converge point-wise a.e.?
August 1st, 2022
examples-counterexamples
real-analysis
measure-theory
convergence-divergence
Example of a Borel measure, which is not Borel-regular
January 8th, 2020
measure-theory
geometric-measure-theory
examples-counterexamples
real-analysis
Intersection of compact sets
August 1st, 2022
metric-spaces
general-topology
examples-counterexamples
proof-explanation
Is total boundedness a topological property?
August 1st, 2022
general-topology
examples-counterexamples
metric-spaces
Example of discontinuous function having all partial derivatives
August 12th, 2020
examples-counterexamples
partial-derivative
multivariable-calculus
Examples of Non-Faithful Group Actions
August 1st, 2022
examples-counterexamples
group-theory
group-actions
The Duality Functor in Linear Algebra
August 1st, 2022
examples-counterexamples
intuition
linear-algebra
category-theory
Change of measure to make things "easier"?
August 1st, 2022
examples-counterexamples
probability
probability-theory
measure-theory
Examples of quasigroups with no identity elements
August 1st, 2022
abstract-algebra
examples-counterexamples
quasigroups
←
1
2
3
4
5
6
7
8
9
10
11
12
…
24
25
→